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{"name": "Math 3 Inverse of Exponential Function with Rational Exponent", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"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": ""}, "name": "Math 3 Inverse of Exponential Function with Rational Exponent", "variable_groups": [], "variablesTest": {"condition": "", "maxRuns": 100}, "extensions": [], "rulesets": {}, "ungrouped_variables": ["base", "a", "b"], "statement": "<p>Find the inverse of the given function:</p>\n<p>$ f(x) = \\simplify{ ( ({base[0]}/{base[1]})^x + {a}&nbsp; )^(1/{b})&nbsp; &nbsp; &nbsp;} $</p>", "metadata": {"licence": "Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International", "description": ""}, "parts": [{"variableReplacementStrategy": "originalfirst", "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "showFeedbackIcon": true, "useCustomName": false, "type": "gapfill", "gaps": [{"checkVariableNames": false, "variableReplacements": [], "checkingAccuracy": 0.001, "showFeedbackIcon": true, "useCustomName": false, "extendBaseMarkingAlgorithm": true, "valuegenerators": [{"value": "", "name": "x"}], "vsetRange": [0, 1], "marks": 1, "answer": "log(x^{b}-{a},{base[0]}/{base[1]})", "variableReplacementStrategy": "originalfirst", "checkingType": "absdiff", "showPreview": true, "type": "jme", "customMarkingAlgorithm": "", "unitTests": [], "scripts": {}, "vsetRangePoints": 5, "showCorrectAnswer": true, "failureRate": 1, "adaptiveMarkingPenalty": 0, "customName": ""}], "customMarkingAlgorithm": "", "unitTests": [], "scripts": {}, "prompt": "<p>The inverse function is:&nbsp;&nbsp;<strong>***&nbsp;enter your answer as log(expression,base) *</strong></p>\n<p>$f^{-1}(x) = $[[0]]</p>", "showCorrectAnswer": true, "adaptiveMarkingPenalty": 0, "marks": 0, "sortAnswers": false, "customName": ""}], "advice": "", "tags": [], "contributors": [{"name": "Terry Young", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3130/"}]}]}], "contributors": [{"name": "Terry Young", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3130/"}]}