// Numbas version: finer_feedback_settings
{"name": "Lois's copy of Functions: composite functions", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"a": {"templateType": "anything", "description": "", "name": "a", "definition": "random(1..8)", "group": "Ungrouped variables"}}, "functions": {}, "parts": [{"prompt": "<p>$(h\\circ f)(x)=\\;$ [[0]]&nbsp;</p>\n<p>$(f\\circ h)(x)=\\;$ [[1]]</p>", "variableReplacementStrategy": "originalfirst", "gaps": [{"answer": "1/(x^2+{a})", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "expectedvariablenames": [], "checkingtype": "absdiff", "scripts": {}, "showCorrectAnswer": true, "checkvariablenames": false, "vsetrangepoints": 5, "answersimplification": "all", "checkingaccuracy": 0.001, "marks": 1, "vsetrange": [0, 1], "type": "jme", "showpreview": true, "showFeedbackIcon": true}, {"answer": "1/(x^2)+{a}", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "expectedvariablenames": [], "checkingtype": "absdiff", "scripts": {}, "showCorrectAnswer": true, "checkvariablenames": false, "vsetrangepoints": 5, "answersimplification": "all", "checkingaccuracy": 0.001, "marks": 1, "vsetrange": [0, 1], "type": "jme", "showpreview": true, "showFeedbackIcon": true}], "variableReplacements": [], "marks": 0, "scripts": {}, "type": "gapfill", "showCorrectAnswer": true, "showFeedbackIcon": true}], "preamble": {"css": "", "js": ""}, "extensions": [], "advice": "<p>Remember that $ (f \\circ h)(x) = f(h(x))$ and &nbsp;$(h \\circ f)(x) = h(f(x)).$</p>", "variable_groups": [], "ungrouped_variables": ["a"], "rulesets": {}, "tags": [], "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>Composite functions.</p>"}, "name": "Lois's copy of Functions: composite functions", "statement": "<p>Let $ f: \\mathbb{R} \\rightarrow \\mathbb{R^+}$ and $h: \\mathbb{R^+} \\rightarrow \\mathbb{R+}$ be mappings with $f(x)=\\simplify{x^2+{a}}$ and $h(x)=\\frac{1}{x}$. Find $(h\\circ f)(x)$ and $(f\\circ h)(x).$</p>", "type": "question", "contributors": [{"name": "Lois Rollings", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/326/"}]}]}], "contributors": [{"name": "Lois Rollings", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/326/"}]}