// Numbas version: finer_feedback_settings
{"name": "2.3.2  Task 1", "extensions": [], "custom_part_types": [], "resources": [["question-resources/HELM2_fig16.png", "/srv/numbas/media/question-resources/HELM2_fig16.png"], ["question-resources/HELM2_fig17.png", "/srv/numbas/media/question-resources/HELM2_fig17.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "2.3.2  Task 1", "tags": [], "metadata": {"description": "<p>Find the inverse of a linear function. Part of HELM book 2.3.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>Find the inverse of the function $f(x) = \\var{a} - \\var{b}x$, using the fact that the inverse function must take an input $7-3x$ and produce an output $x$. So $f^{-1}(\\var{a}-\\var{b}x) = x$</p>", "advice": "<p>Let $z = \\var{a}-\\var{b}x$</p>\n<p>$ \\var{b}x = \\var{a} - z$</p>\n<p>$x = \\dfrac{\\var{a}-z}{\\var{b}}$</p>\n<p>So $f^{-1}(z) = \\dfrac{\\var{a}-z}{\\var{b}}$</p>\n<p>and thus $f^{-1}(x) = \\dfrac{\\var{a}-x}{\\var{b}}$</p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "random(2..9)", "description": "", "templateType": "anything", "can_override": false}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(2..9)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "b"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Introduce a new variable $z$ so that $z = \\var{a} - \\var{b}x$ and transpose this to find $x$. Hence write down the inverse function:</p>\n<p>$f^{-1}(x) = $ [[0]]</p>", "gaps": [{"type": "jme", "useCustomName": true, "customName": "inverse function", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "({a}-x)/{b}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "x", "value": ""}]}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question", "contributors": [{"name": "Merryn Horrocks", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4052/"}]}]}], "contributors": [{"name": "Merryn Horrocks", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4052/"}]}