// Numbas version: exam_results_page_options {"percentPass": "80", "question_groups": [{"pickQuestions": 1, "pickingStrategy": "all-shuffled", "name": "Group", "questions": [{"name": "Math 3 Inverse Exponential Function", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Terry Young", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3130/"}], "variables": {"a": {"definition": "random(1..10)", "group": "Ungrouped variables", "templateType": "anything", "name": "a", "description": ""}, "choice": {"definition": "(signb+1)/2", "group": "Ungrouped variables", "templateType": "anything", "name": "choice", "description": ""}, "operator": {"definition": "[\"+\",\"-\"]", "group": "Ungrouped variables", "templateType": "anything", "name": "operator", "description": ""}, "base": {"definition": "random(2..15)", "group": "Ungrouped variables", "templateType": "anything", "name": "base", "description": ""}, "signb": {"definition": "sign(b)", "group": "Ungrouped variables", "templateType": "anything", "name": "signb", "description": ""}, "b": {"definition": "random(-20..20)", "group": "Ungrouped variables", "templateType": "anything", "name": "b", "description": ""}}, "functions": {}, "preamble": {"js": "", "css": ""}, "variable_groups": [], "variablesTest": {"condition": "", "maxRuns": 100}, "rulesets": {}, "ungrouped_variables": ["base", "a", "b", "signb", "choice", "operator"], "statement": "

Find the inverse of the given function:

\n

$y = \\simplify{ {base}^(x/{a}) +{b}}  $ 

", "metadata": {"licence": "Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International", "description": ""}, "parts": [{"variableReplacementStrategy": "originalfirst", "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "showFeedbackIcon": true, "useCustomName": false, "type": "gapfill", "gaps": [{"checkVariableNames": false, "variableReplacements": [], "checkingAccuracy": 0.001, "showFeedbackIcon": true, "useCustomName": false, "extendBaseMarkingAlgorithm": true, "valuegenerators": [{"value": "", "name": "x"}], "vsetRange": [0, 1], "marks": 1, "answer": "log((x-{b})^{a},{base})", "variableReplacementStrategy": "originalfirst", "checkingType": "absdiff", "showPreview": true, "type": "jme", "customMarkingAlgorithm": "", "unitTests": [], "scripts": {}, "vsetRangePoints": 5, "showCorrectAnswer": true, "failureRate": 1, "adaptiveMarkingPenalty": 0, "customName": ""}], "customMarkingAlgorithm": "", "unitTests": [], "scripts": {}, "prompt": "

The inverse function is: *** enter $\\log_{3}(x-5)$ as --> log(x-5,3) ***

\n

$f^{-1}(x) = $[[0]]

", "showCorrectAnswer": true, "adaptiveMarkingPenalty": 0, "marks": 0, "sortAnswers": false, "customName": ""}], "advice": "", "tags": []}, {"name": "Math 3 Inverse Log Function", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Terry Young", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3130/"}], "advice": "", "rulesets": {}, "ungrouped_variables": ["base", "a", "b", "c"], "variablesTest": {"condition": "", "maxRuns": 100}, "preamble": {"css": "", "js": ""}, "functions": {}, "tags": [], "variables": {"b": {"definition": "random(-20..20)", "group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "b"}, "a": {"definition": "random(-10..10 except 0)", "group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "a"}, "base": {"definition": "random(2..15)", "group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "base"}, "c": {"definition": "random(-25..25)", "group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "c"}}, "statement": "

Find the inverse of the given function:

\n

$y =  \\log_{\\var{base}} (\\simplify{ {a}x+{b}}) + \\var{c} $

", "metadata": {"licence": "Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International", "description": ""}, "parts": [{"prompt": "

The inverse function is:  $f^{-1}(x)= $ [[0]]

", "marks": 0, "customName": "", "adaptiveMarkingPenalty": 0, "showCorrectAnswer": true, "unitTests": [], "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "scripts": {}, "type": "gapfill", "sortAnswers": false, "showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "useCustomName": false, "gaps": [{"customName": "", "unitTests": [], "checkingAccuracy": 0.001, "variableReplacements": [], "showPreview": true, "scripts": {}, "type": "jme", "showFeedbackIcon": true, "useCustomName": false, "marks": 1, "adaptiveMarkingPenalty": 0, "showCorrectAnswer": true, "answer": "({base}^(x-{c})-{b})/{a}", "failureRate": "2", "variableReplacementStrategy": "originalfirst", "checkingType": "absdiff", "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "valuegenerators": [{"value": "", "name": "x"}]}]}], "variable_groups": []}, {"name": "Math 3 Inverse Log Function", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Terry Young", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3130/"}], "advice": "", "rulesets": {}, "ungrouped_variables": ["base", "a", "b", "c"], "variablesTest": {"condition": "", "maxRuns": 100}, "preamble": {"css": "", "js": ""}, "functions": {}, "tags": [], "variables": {"b": {"definition": "random(-20..20)", "group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "b"}, "a": {"definition": "random(-10..10 except 0)", "group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "a"}, "base": {"definition": "random(2..15)", "group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "base"}, "c": {"definition": "random(-25..25)", "group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "c"}}, "statement": "

Find the inverse of the given function:

\n

$y =  \\log_{\\var{base}} (\\simplify{ {a}x+{b}}) + \\var{c} $

", "metadata": {"licence": "Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International", "description": ""}, "parts": [{"prompt": "

The inverse function is:  $f^{-1}(x)= $ [[0]]

", "marks": 0, "customName": "", "adaptiveMarkingPenalty": 0, "showCorrectAnswer": true, "unitTests": [], "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "scripts": {}, "type": "gapfill", "sortAnswers": false, "showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "useCustomName": false, "gaps": [{"customName": "", "unitTests": [], "checkingAccuracy": 0.001, "variableReplacements": [], "showPreview": true, "scripts": {}, "type": "jme", "showFeedbackIcon": true, "useCustomName": false, "marks": 1, "adaptiveMarkingPenalty": 0, "showCorrectAnswer": true, "answer": "({base}^(x-{c})-{b})/{a}", "failureRate": "2", "variableReplacementStrategy": "originalfirst", "checkingType": "absdiff", "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "valuegenerators": [{"value": "", "name": "x"}]}]}], "variable_groups": []}, {"name": "Math 3 Inverse Log Function", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Terry Young", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3130/"}], "advice": "", "rulesets": {}, "ungrouped_variables": ["base", "a", "b", "c"], "variablesTest": {"condition": "", "maxRuns": 100}, "preamble": {"css": "", "js": ""}, "functions": {}, "tags": [], "variables": {"b": {"definition": "random(-20..20)", "group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "b"}, "a": {"definition": "random(-10..10 except 0)", "group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "a"}, "base": {"definition": "random(2..15)", "group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "base"}, "c": {"definition": "random(-25..25)", "group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "c"}}, "statement": "

Find the inverse of the given function:

\n

$y =  \\log_{\\var{base}} (\\simplify{ {a}x+{b}}) + \\var{c} $

", "metadata": {"licence": "Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International", "description": ""}, "parts": [{"prompt": "

The inverse function is:  $f^{-1}(x)= $ [[0]]

", "marks": 0, "customName": "", "adaptiveMarkingPenalty": 0, "showCorrectAnswer": true, "unitTests": [], "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "scripts": {}, "type": "gapfill", "sortAnswers": false, "showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "useCustomName": false, "gaps": [{"customName": "", "unitTests": [], "checkingAccuracy": 0.001, "variableReplacements": [], "showPreview": true, "scripts": {}, "type": "jme", "showFeedbackIcon": true, "useCustomName": false, "marks": 1, "adaptiveMarkingPenalty": 0, "showCorrectAnswer": true, "answer": "({base}^(x-{c})-{b})/{a}", "failureRate": "2", "variableReplacementStrategy": "originalfirst", "checkingType": "absdiff", "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "valuegenerators": [{"value": "", "name": "x"}]}]}], "variable_groups": []}, {"name": "Math 3 Inverse Exponential Function", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Terry Young", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3130/"}], "variables": {"a": {"definition": "random(1..10)", "group": "Ungrouped variables", "templateType": "anything", "name": "a", "description": ""}, "choice": {"definition": "(signb+1)/2", "group": "Ungrouped variables", "templateType": "anything", "name": "choice", "description": ""}, "operator": {"definition": "[\"+\",\"-\"]", "group": "Ungrouped variables", "templateType": "anything", "name": "operator", "description": ""}, "base": {"definition": "random(2..15)", "group": "Ungrouped variables", "templateType": "anything", "name": "base", "description": ""}, "signb": {"definition": "sign(b)", "group": "Ungrouped variables", "templateType": "anything", "name": "signb", "description": ""}, "b": {"definition": "random(-20..20)", "group": "Ungrouped variables", "templateType": "anything", "name": "b", "description": ""}}, "functions": {}, "preamble": {"js": "", "css": ""}, "variable_groups": [], "variablesTest": {"condition": "", "maxRuns": 100}, "rulesets": {}, "ungrouped_variables": ["base", "a", "b", "signb", "choice", "operator"], "statement": "

Find the inverse of the given function:

\n

$y = \\simplify{ {base}^(x/{a}) +{b}}  $ 

", "metadata": {"licence": "Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International", "description": ""}, "parts": [{"variableReplacementStrategy": "originalfirst", "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "showFeedbackIcon": true, "useCustomName": false, "type": "gapfill", "gaps": [{"checkVariableNames": false, "variableReplacements": [], "checkingAccuracy": 0.001, "showFeedbackIcon": true, "useCustomName": false, "extendBaseMarkingAlgorithm": true, "valuegenerators": [{"value": "", "name": "x"}], "vsetRange": [0, 1], "marks": 1, "answer": "log((x-{b})^{a},{base})", "variableReplacementStrategy": "originalfirst", "checkingType": "absdiff", "showPreview": true, "type": "jme", "customMarkingAlgorithm": "", "unitTests": [], "scripts": {}, "vsetRangePoints": 5, "showCorrectAnswer": true, "failureRate": 1, "adaptiveMarkingPenalty": 0, "customName": ""}], "customMarkingAlgorithm": "", "unitTests": [], "scripts": {}, "prompt": "

The inverse function is: *** enter $\\log_{3}(x-5)$ as --> log(x-5,3) ***

\n

$f^{-1}(x) = $[[0]]

", "showCorrectAnswer": true, "adaptiveMarkingPenalty": 0, "marks": 0, "sortAnswers": false, "customName": ""}], "advice": "", "tags": []}, {"name": "Math 3 Inverse Exponential Function", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Terry Young", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3130/"}], "variables": {"a": {"definition": "random(1..10)", "group": "Ungrouped variables", "templateType": "anything", "name": "a", "description": ""}, "choice": {"definition": "(signb+1)/2", "group": "Ungrouped variables", "templateType": "anything", "name": "choice", "description": ""}, "operator": {"definition": "[\"+\",\"-\"]", "group": "Ungrouped variables", "templateType": "anything", "name": "operator", "description": ""}, "base": {"definition": "random(2..15)", "group": "Ungrouped variables", "templateType": "anything", "name": "base", "description": ""}, "signb": {"definition": "sign(b)", "group": "Ungrouped variables", "templateType": "anything", "name": "signb", "description": ""}, "b": {"definition": "random(-20..20)", "group": "Ungrouped variables", "templateType": "anything", "name": "b", "description": ""}}, "functions": {}, "preamble": {"js": "", "css": ""}, "variable_groups": [], "variablesTest": {"condition": "", "maxRuns": 100}, "rulesets": {}, "ungrouped_variables": ["base", "a", "b", "signb", "choice", "operator"], "statement": "

Find the inverse of the given function:

\n

$y = \\simplify{ {base}^(x/{a}) +{b}}  $ 

", "metadata": {"licence": "Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International", "description": ""}, "parts": [{"variableReplacementStrategy": "originalfirst", "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "showFeedbackIcon": true, "useCustomName": false, "type": "gapfill", "gaps": [{"checkVariableNames": false, "variableReplacements": [], "checkingAccuracy": 0.001, "showFeedbackIcon": true, "useCustomName": false, "extendBaseMarkingAlgorithm": true, "valuegenerators": [{"value": "", "name": "x"}], "vsetRange": [0, 1], "marks": 1, "answer": "log((x-{b})^{a},{base})", "variableReplacementStrategy": "originalfirst", "checkingType": "absdiff", "showPreview": true, "type": "jme", "customMarkingAlgorithm": "", "unitTests": [], "scripts": {}, "vsetRangePoints": 5, "showCorrectAnswer": true, "failureRate": 1, "adaptiveMarkingPenalty": 0, "customName": ""}], "customMarkingAlgorithm": "", "unitTests": [], "scripts": {}, "prompt": "

The inverse function is: *** enter $\\log_{3}(x-5)$ as --> log(x-5,3) ***

\n

$f^{-1}(x) = $[[0]]

", "showCorrectAnswer": true, "adaptiveMarkingPenalty": 0, "marks": 0, "sortAnswers": false, "customName": ""}], "advice": "", "tags": []}, {"name": "Math 3 Inverse Exponential Function", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Terry Young", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3130/"}], "variables": {"a": {"definition": "random(1..10)", "group": "Ungrouped variables", "templateType": "anything", "name": "a", "description": ""}, "choice": {"definition": "(signb+1)/2", "group": "Ungrouped variables", "templateType": "anything", "name": "choice", "description": ""}, "operator": {"definition": "[\"+\",\"-\"]", "group": "Ungrouped variables", "templateType": "anything", "name": "operator", "description": ""}, "base": {"definition": "random(2..15)", "group": "Ungrouped variables", "templateType": "anything", "name": "base", "description": ""}, "signb": {"definition": "sign(b)", "group": "Ungrouped variables", "templateType": "anything", "name": "signb", "description": ""}, "b": {"definition": "random(-20..20)", "group": "Ungrouped variables", "templateType": "anything", "name": "b", "description": ""}}, "functions": {}, "preamble": {"js": "", "css": ""}, "variable_groups": [], "variablesTest": {"condition": "", "maxRuns": 100}, "rulesets": {}, "ungrouped_variables": ["base", "a", "b", "signb", "choice", "operator"], "statement": "

Find the inverse of the given function:

\n

$y = \\simplify{ {base}^(x/{a}) +{b}}  $ 

", "metadata": {"licence": "Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International", "description": ""}, "parts": [{"variableReplacementStrategy": "originalfirst", "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "showFeedbackIcon": true, "useCustomName": false, "type": "gapfill", "gaps": [{"checkVariableNames": false, "variableReplacements": [], "checkingAccuracy": 0.001, "showFeedbackIcon": true, "useCustomName": false, "extendBaseMarkingAlgorithm": true, "valuegenerators": [{"value": "", "name": "x"}], "vsetRange": [0, 1], "marks": 1, "answer": "log((x-{b})^{a},{base})", "variableReplacementStrategy": "originalfirst", "checkingType": "absdiff", "showPreview": true, "type": "jme", "customMarkingAlgorithm": "", "unitTests": [], "scripts": {}, "vsetRangePoints": 5, "showCorrectAnswer": true, "failureRate": 1, "adaptiveMarkingPenalty": 0, "customName": ""}], "customMarkingAlgorithm": "", "unitTests": [], "scripts": {}, "prompt": "

The inverse function is: *** enter $\\log_{3}(x-5)$ as --> log(x-5,3) ***

\n

$f^{-1}(x) = $[[0]]

", "showCorrectAnswer": true, "adaptiveMarkingPenalty": 0, "marks": 0, "sortAnswers": false, "customName": ""}], "advice": "", "tags": []}, {"name": "Math 3 Inverse Exponential Function", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Terry Young", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3130/"}], "variables": {"a": {"definition": "random(1..10)", "group": "Ungrouped variables", "templateType": "anything", "name": "a", "description": ""}, "choice": {"definition": "(signb+1)/2", "group": "Ungrouped variables", "templateType": "anything", "name": "choice", "description": ""}, "operator": {"definition": "[\"+\",\"-\"]", "group": "Ungrouped variables", "templateType": "anything", "name": "operator", "description": ""}, "base": {"definition": "random(2..15)", "group": "Ungrouped variables", "templateType": "anything", "name": "base", "description": ""}, "signb": {"definition": "sign(b)", "group": "Ungrouped variables", "templateType": "anything", "name": "signb", "description": ""}, "b": {"definition": "random(-20..20)", "group": "Ungrouped variables", "templateType": "anything", "name": "b", "description": ""}}, "functions": {}, "preamble": {"js": "", "css": ""}, "variable_groups": [], "variablesTest": {"condition": "", "maxRuns": 100}, "rulesets": {}, "ungrouped_variables": ["base", "a", "b", "signb", "choice", "operator"], "statement": "

Find the inverse of the given function:

\n

$y = \\simplify{ {base}^(x/{a}) +{b}}  $ 

", "metadata": {"licence": "Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International", "description": ""}, "parts": [{"variableReplacementStrategy": "originalfirst", "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "showFeedbackIcon": true, "useCustomName": false, "type": "gapfill", "gaps": [{"checkVariableNames": false, "variableReplacements": [], "checkingAccuracy": 0.001, "showFeedbackIcon": true, "useCustomName": false, "extendBaseMarkingAlgorithm": true, "valuegenerators": [{"value": "", "name": "x"}], "vsetRange": [0, 1], "marks": 1, "answer": "log((x-{b})^{a},{base})", "variableReplacementStrategy": "originalfirst", "checkingType": "absdiff", "showPreview": true, "type": "jme", "customMarkingAlgorithm": "", "unitTests": [], "scripts": {}, "vsetRangePoints": 5, "showCorrectAnswer": true, "failureRate": 1, "adaptiveMarkingPenalty": 0, "customName": ""}], "customMarkingAlgorithm": "", "unitTests": [], "scripts": {}, "prompt": "

The inverse function is: *** enter $\\log_{3}(x-5)$ as --> log(x-5,3) ***

\n

$f^{-1}(x) = $[[0]]

", "showCorrectAnswer": true, "adaptiveMarkingPenalty": 0, "marks": 0, "sortAnswers": false, "customName": ""}], "advice": "", "tags": []}, {"name": "Math 3 Inverse of Exponential Function with Rational Exponent", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Terry Young", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3130/"}], "variables": {"base": {"definition": "rational_approximation(random(0.05..9#0.01))", "group": "Ungrouped variables", "templateType": "anything", "name": "base", "description": ""}, "a": {"definition": "random(-25..25 except 0)", "group": "Ungrouped variables", "templateType": "anything", "name": "a", "description": ""}, "b": {"definition": "random(2..9)", "group": "Ungrouped variables", "templateType": "anything", "name": "b", "description": ""}}, "functions": {}, "preamble": {"js": "", "css": ""}, "variable_groups": [], "variablesTest": {"condition": "", "maxRuns": 100}, "rulesets": {}, "ungrouped_variables": ["base", "a", "b"], "statement": "

Find the inverse of the given function:

\n

$ f(x) = \\simplify{ ( ({base[0]}/{base[1]})^x + {a}  )^(1/{b})     } $

", "metadata": {"licence": "Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International", "description": ""}, "parts": [{"variableReplacementStrategy": "originalfirst", "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "showFeedbackIcon": true, "useCustomName": false, "type": "gapfill", "gaps": [{"checkVariableNames": false, "variableReplacements": [], "checkingAccuracy": 0.001, "showFeedbackIcon": true, "useCustomName": false, "extendBaseMarkingAlgorithm": true, "valuegenerators": [{"value": "", "name": "x"}], "vsetRange": [0, 1], "marks": 1, "answer": "log(x^{b}-{a},{base[0]}/{base[1]})", "variableReplacementStrategy": "originalfirst", "checkingType": "absdiff", "showPreview": true, "type": "jme", "customMarkingAlgorithm": "", "unitTests": [], "scripts": {}, "vsetRangePoints": 5, "showCorrectAnswer": true, "failureRate": 1, "adaptiveMarkingPenalty": 0, "customName": ""}], "customMarkingAlgorithm": "", "unitTests": [], "scripts": {}, "prompt": "

The inverse function is:  *** enter your answer as log(expression,base) *

\n

$f^{-1}(x) = $[[0]]

", "showCorrectAnswer": true, "adaptiveMarkingPenalty": 0, "marks": 0, "sortAnswers": false, "customName": ""}], "advice": "", "tags": []}, {"name": "Math 3 Inverse of Exponential Function with Rational Exponent", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Terry Young", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3130/"}], "variables": {"base": {"definition": "rational_approximation(random(0.05..9#0.01))", "group": "Ungrouped variables", "templateType": "anything", "name": "base", "description": ""}, "a": {"definition": "random(-25..25 except 0)", "group": "Ungrouped variables", "templateType": "anything", "name": "a", "description": ""}, "b": {"definition": "random(2..9)", "group": "Ungrouped variables", "templateType": "anything", "name": "b", "description": ""}}, "functions": {}, "preamble": {"js": "", "css": ""}, "variable_groups": [], "variablesTest": {"condition": "", "maxRuns": 100}, "rulesets": {}, "ungrouped_variables": ["base", "a", "b"], "statement": "

Find the inverse of the given function:

\n

$ f(x) = \\simplify{ ( ({base[0]}/{base[1]})^x + {a}  )^(1/{b})     } $

", "metadata": {"licence": "Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International", "description": ""}, "parts": [{"variableReplacementStrategy": "originalfirst", "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "showFeedbackIcon": true, "useCustomName": false, "type": "gapfill", "gaps": [{"checkVariableNames": false, "variableReplacements": [], "checkingAccuracy": 0.001, "showFeedbackIcon": true, "useCustomName": false, "extendBaseMarkingAlgorithm": true, "valuegenerators": [{"value": "", "name": "x"}], "vsetRange": [0, 1], "marks": 1, "answer": "log(x^{b}-{a},{base[0]}/{base[1]})", "variableReplacementStrategy": "originalfirst", "checkingType": "absdiff", "showPreview": true, "type": "jme", "customMarkingAlgorithm": "", "unitTests": [], "scripts": {}, "vsetRangePoints": 5, "showCorrectAnswer": true, "failureRate": 1, "adaptiveMarkingPenalty": 0, "customName": ""}], "customMarkingAlgorithm": "", "unitTests": [], "scripts": {}, "prompt": "

The inverse function is:  *** enter your answer as log(expression,base) *

\n

$f^{-1}(x) = $[[0]]

", "showCorrectAnswer": true, "adaptiveMarkingPenalty": 0, "marks": 0, "sortAnswers": false, "customName": ""}], "advice": "", "tags": []}, {"name": "Math 3 Inverse of Exponential Function with Rational Exponent", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Terry Young", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3130/"}], "variables": {"base": {"definition": "rational_approximation(random(0.05..9#0.01))", "group": "Ungrouped variables", "templateType": "anything", "name": "base", "description": ""}, "a": {"definition": "random(-25..25 except 0)", "group": "Ungrouped variables", "templateType": "anything", "name": "a", "description": ""}, "b": {"definition": "random(2..9)", "group": "Ungrouped variables", "templateType": "anything", "name": "b", "description": ""}}, "functions": {}, "preamble": {"js": "", "css": ""}, "variable_groups": [], "variablesTest": {"condition": "", "maxRuns": 100}, "rulesets": {}, "ungrouped_variables": ["base", "a", "b"], "statement": "

Find the inverse of the given function:

\n

$ f(x) = \\simplify{ ( ({base[0]}/{base[1]})^x + {a}  )^(1/{b})     } $

", "metadata": {"licence": "Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International", "description": ""}, "parts": [{"variableReplacementStrategy": "originalfirst", "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "showFeedbackIcon": true, "useCustomName": false, "type": "gapfill", "gaps": [{"checkVariableNames": false, "variableReplacements": [], "checkingAccuracy": 0.001, "showFeedbackIcon": true, "useCustomName": false, "extendBaseMarkingAlgorithm": true, "valuegenerators": [{"value": "", "name": "x"}], "vsetRange": [0, 1], "marks": 1, "answer": "log(x^{b}-{a},{base[0]}/{base[1]})", "variableReplacementStrategy": "originalfirst", "checkingType": "absdiff", "showPreview": true, "type": "jme", "customMarkingAlgorithm": "", "unitTests": [], "scripts": {}, "vsetRangePoints": 5, "showCorrectAnswer": true, "failureRate": 1, "adaptiveMarkingPenalty": 0, "customName": ""}], "customMarkingAlgorithm": "", "unitTests": [], "scripts": {}, "prompt": "

The inverse function is:  *** enter your answer as log(expression,base) *

\n

$f^{-1}(x) = $[[0]]

", "showCorrectAnswer": true, "adaptiveMarkingPenalty": 0, "marks": 0, "sortAnswers": false, "customName": ""}], "advice": "", "tags": []}, {"name": "Math 3 Inverse of Log function with rational exponent", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Terry Young", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3130/"}], "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"js": "", "css": ""}, "variable_groups": [], "tags": [], "ungrouped_variables": ["base", "a", "b", "c"], "rulesets": {}, "functions": {}, "parts": [{"customName": "", "customMarkingAlgorithm": "", "variableReplacementStrategy": "originalfirst", "sortAnswers": false, "adaptiveMarkingPenalty": 0, "showCorrectAnswer": true, "useCustomName": false, "showFeedbackIcon": true, "unitTests": [], "extendBaseMarkingAlgorithm": true, "marks": 0, "type": "gapfill", "scripts": {}, "gaps": [{"showPreview": true, "adaptiveMarkingPenalty": 0, "useCustomName": false, "unitTests": [], "extendBaseMarkingAlgorithm": true, "checkVariableNames": false, "marks": 1, "failureRate": 1, "variableReplacementStrategy": "originalfirst", "answer": "(({base}^x-{c})/{a})^(1/{b})", "customName": "", "customMarkingAlgorithm": "", "showCorrectAnswer": true, "showFeedbackIcon": true, "vsetRangePoints": 5, "variableReplacements": [], "checkingAccuracy": 0.001, "type": "jme", "valuegenerators": [{"value": "", "name": "x"}], "scripts": {}, "vsetRange": [0, 1], "checkingType": "absdiff"}], "variableReplacements": [], "prompt": "

The inverse of the function is:

\n

$f^{-1}(x) = $[[0]]

"}], "metadata": {"description": "", "licence": "Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International"}, "variables": {"c": {"group": "Ungrouped variables", "definition": "random(-15..15 except 0)", "description": "", "templateType": "anything", "name": "c"}, "base": {"group": "Ungrouped variables", "definition": "random(2..9)", "description": "", "templateType": "anything", "name": "base"}, "a": {"group": "Ungrouped variables", "definition": "random(1..15)", "description": "", "templateType": "anything", "name": "a"}, "b": {"group": "Ungrouped variables", "definition": "random(2..15)", "description": "", "templateType": "anything", "name": "b"}}, "statement": "

Find the inverse of the given function:

\n

$f(x) = \\log_\\var{base}(\\simplify{ {a}x^{b}+{c} })  $

", "advice": ""}, {"name": "Math 3 Inverse of Log function with rational exponent", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Terry Young", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3130/"}], "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"js": "", "css": ""}, "variable_groups": [], "tags": [], "ungrouped_variables": ["base", "a", "b", "c"], "rulesets": {}, "functions": {}, "parts": [{"customName": "", "customMarkingAlgorithm": "", "variableReplacementStrategy": "originalfirst", "sortAnswers": false, "adaptiveMarkingPenalty": 0, "showCorrectAnswer": true, "useCustomName": false, "showFeedbackIcon": true, "unitTests": [], "extendBaseMarkingAlgorithm": true, "marks": 0, "type": "gapfill", "scripts": {}, "gaps": [{"showPreview": true, "adaptiveMarkingPenalty": 0, "useCustomName": false, "unitTests": [], "extendBaseMarkingAlgorithm": true, "checkVariableNames": false, "marks": 1, "failureRate": 1, "variableReplacementStrategy": "originalfirst", "answer": "(({base}^x-{c})/{a})^(1/{b})", "customName": "", "customMarkingAlgorithm": "", "showCorrectAnswer": true, "showFeedbackIcon": true, "vsetRangePoints": 5, "variableReplacements": [], "checkingAccuracy": 0.001, "type": "jme", "valuegenerators": [{"value": "", "name": "x"}], "scripts": {}, "vsetRange": [0, 1], "checkingType": "absdiff"}], "variableReplacements": [], "prompt": "

The inverse of the function is:

\n

$f^{-1}(x) = $[[0]]

"}], "metadata": {"description": "", "licence": "Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International"}, "variables": {"c": {"group": "Ungrouped variables", "definition": "random(-15..15 except 0)", "description": "", "templateType": "anything", "name": "c"}, "base": {"group": "Ungrouped variables", "definition": "random(2..9)", "description": "", "templateType": "anything", "name": "base"}, "a": {"group": "Ungrouped variables", "definition": "random(1..15)", "description": "", "templateType": "anything", "name": "a"}, "b": {"group": "Ungrouped variables", "definition": "random(2..15)", "description": "", "templateType": "anything", "name": "b"}}, "statement": "

Find the inverse of the given function:

\n

$f(x) = \\log_\\var{base}(\\simplify{ {a}x^{b}+{c} })  $

", "advice": ""}, {"name": "Math 3 Inverse of Log function with rational exponent", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Terry Young", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3130/"}], "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"js": "", "css": ""}, "variable_groups": [], "tags": [], "ungrouped_variables": ["base", "a", "b", "c"], "rulesets": {}, "functions": {}, "parts": [{"customName": "", "customMarkingAlgorithm": "", "variableReplacementStrategy": "originalfirst", "sortAnswers": false, "adaptiveMarkingPenalty": 0, "showCorrectAnswer": true, "useCustomName": false, "showFeedbackIcon": true, "unitTests": [], "extendBaseMarkingAlgorithm": true, "marks": 0, "type": "gapfill", "scripts": {}, "gaps": [{"showPreview": true, "adaptiveMarkingPenalty": 0, "useCustomName": false, "unitTests": [], "extendBaseMarkingAlgorithm": true, "checkVariableNames": false, "marks": 1, "failureRate": 1, "variableReplacementStrategy": "originalfirst", "answer": "(({base}^x-{c})/{a})^(1/{b})", "customName": "", "customMarkingAlgorithm": "", "showCorrectAnswer": true, "showFeedbackIcon": true, "vsetRangePoints": 5, "variableReplacements": [], "checkingAccuracy": 0.001, "type": "jme", "valuegenerators": [{"value": "", "name": "x"}], "scripts": {}, "vsetRange": [0, 1], "checkingType": "absdiff"}], "variableReplacements": [], "prompt": "

The inverse of the function is:

\n

$f^{-1}(x) = $[[0]]

"}], "metadata": {"description": "", "licence": "Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International"}, "variables": {"c": {"group": "Ungrouped variables", "definition": "random(-15..15 except 0)", "description": "", "templateType": "anything", "name": "c"}, "base": {"group": "Ungrouped variables", "definition": "random(2..9)", "description": "", "templateType": "anything", "name": "base"}, "a": {"group": "Ungrouped variables", "definition": "random(1..15)", "description": "", "templateType": "anything", "name": "a"}, "b": {"group": "Ungrouped variables", "definition": "random(2..15)", "description": "", "templateType": "anything", "name": "b"}}, "statement": "

Find the inverse of the given function:

\n

$f(x) = \\log_\\var{base}(\\simplify{ {a}x^{b}+{c} })  $

", "advice": ""}, {"name": "Math 3 Inverse of Log function with rational exponent", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Terry Young", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3130/"}], "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"js": "", "css": ""}, "variable_groups": [], "tags": [], "ungrouped_variables": ["base", "a", "b", "c"], "rulesets": {}, "functions": {}, "parts": [{"customName": "", "customMarkingAlgorithm": "", "variableReplacementStrategy": "originalfirst", "sortAnswers": false, "adaptiveMarkingPenalty": 0, "showCorrectAnswer": true, "useCustomName": false, "showFeedbackIcon": true, "unitTests": [], "extendBaseMarkingAlgorithm": true, "marks": 0, "type": "gapfill", "scripts": {}, "gaps": [{"showPreview": true, "adaptiveMarkingPenalty": 0, "useCustomName": false, "unitTests": [], "extendBaseMarkingAlgorithm": true, "checkVariableNames": false, "marks": 1, "failureRate": 1, "variableReplacementStrategy": "originalfirst", "answer": "(({base}^x-{c})/{a})^(1/{b})", "customName": "", "customMarkingAlgorithm": "", "showCorrectAnswer": true, "showFeedbackIcon": true, "vsetRangePoints": 5, "variableReplacements": [], "checkingAccuracy": 0.001, "type": "jme", "valuegenerators": [{"value": "", "name": "x"}], "scripts": {}, "vsetRange": [0, 1], "checkingType": "absdiff"}], "variableReplacements": [], "prompt": "

The inverse of the function is:

\n

$f^{-1}(x) = $[[0]]

"}], "metadata": {"description": "", "licence": "Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International"}, "variables": {"c": {"group": "Ungrouped variables", "definition": "random(-15..15 except 0)", "description": "", "templateType": "anything", "name": "c"}, "base": {"group": "Ungrouped variables", "definition": "random(2..9)", "description": "", "templateType": "anything", "name": "base"}, "a": {"group": "Ungrouped variables", "definition": "random(1..15)", "description": "", "templateType": "anything", "name": "a"}, "b": {"group": "Ungrouped variables", "definition": "random(2..15)", "description": "", "templateType": "anything", "name": "b"}}, "statement": "

Find the inverse of the given function:

\n

$f(x) = \\log_\\var{base}(\\simplify{ {a}x^{b}+{c} })  $

", "advice": ""}, {"name": "Math 3 Inverse of Exponential Function with Rational Exponent", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Terry Young", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3130/"}], "variables": {"base": {"definition": "rational_approximation(random(0.05..9#0.01))", "group": "Ungrouped variables", "templateType": "anything", "name": "base", "description": ""}, "a": {"definition": "random(-25..25 except 0)", "group": "Ungrouped variables", "templateType": "anything", "name": "a", "description": ""}, "b": {"definition": "random(2..9)", "group": "Ungrouped variables", "templateType": "anything", "name": "b", "description": ""}}, "functions": {}, "preamble": {"js": "", "css": ""}, "variable_groups": [], "variablesTest": {"condition": "", "maxRuns": 100}, "rulesets": {}, "ungrouped_variables": ["base", "a", "b"], "statement": "

Find the inverse of the given function:

\n

$ f(x) = \\simplify{ ( ({base[0]}/{base[1]})^x + {a}  )^(1/{b})     } $

", "metadata": {"licence": "Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International", "description": ""}, "parts": [{"variableReplacementStrategy": "originalfirst", "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "showFeedbackIcon": true, "useCustomName": false, "type": "gapfill", "gaps": [{"checkVariableNames": false, "variableReplacements": [], "checkingAccuracy": 0.001, "showFeedbackIcon": true, "useCustomName": false, "extendBaseMarkingAlgorithm": true, "valuegenerators": [{"value": "", "name": "x"}], "vsetRange": [0, 1], "marks": 1, "answer": "log(x^{b}-{a},{base[0]}/{base[1]})", "variableReplacementStrategy": "originalfirst", "checkingType": "absdiff", "showPreview": true, "type": "jme", "customMarkingAlgorithm": "", "unitTests": [], "scripts": {}, "vsetRangePoints": 5, "showCorrectAnswer": true, "failureRate": 1, "adaptiveMarkingPenalty": 0, "customName": ""}], "customMarkingAlgorithm": "", "unitTests": [], "scripts": {}, "prompt": "

The inverse function is:  *** enter your answer as log(expression,base) *

\n

$f^{-1}(x) = $[[0]]

", "showCorrectAnswer": true, "adaptiveMarkingPenalty": 0, "marks": 0, "sortAnswers": false, "customName": ""}], "advice": "", "tags": []}]}], "showstudentname": true, "feedback": {"allowrevealanswer": true, "showactualmark": true, "feedbackmessages": [], "advicethreshold": 0, "showtotalmark": true, "intro": "", "showanswerstate": true}, "metadata": {"description": "Students will find the inverse of log and exponential functions.", "licence": "Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International"}, "duration": 0, "showQuestionGroupNames": false, "timing": {"allowPause": true, "timedwarning": {"action": "none", "message": ""}, "timeout": {"action": "none", "message": ""}}, "navigation": {"startpassword": "", "preventleave": true, "onleave": {"action": "none", "message": ""}, "browse": true, "allowsteps": true, "allowregen": true, "showfrontpage": true, "reverse": true, "showresultspage": "oncompletion"}, "name": "Math 3 CW Logarithmic Function and Its Inverse", "contributors": [{"name": "Terry Young", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3130/"}], "extensions": [], "custom_part_types": [], "resources": []}