IB›IB Maths: Analysis and Approaches HL›Mind maps2.2 Functions, domain, range and inverseIB Maths: Analysis and Approaches HL: Mind mapStudy pack PDFAlso for this subtopic:Revision notesFlashcardsSubtopic testCover factsWhat is a function?One output for each inputDomain = allowed inputs (xxx)Range = outputs produced (f(x)f(x)f(x))Vertical line test at most one intersectionx−3\sqrt{x-3}x−3 needs x≥3x \ge 3x≥3Notation, modelsC(12)C(12)C(12) means substitute 12, not C×12C \times 12C×12Model domain must make sense in contextRange on an interval: use values at both endsWatch strict and non-strict inequalitiesInverse functionf(a)=bf(a) = bf(a)=b means f−1(b)=af^{-1}(b) = af−1(b)=aSolving f(x)=bf(x) = bf(x)=b is finding f−1(b)f^{-1}(b)f−1(b)Method: write y=f(x)y = f(x)y=f(x), swap xxx and yyyRearrange for yyyFunctionsdomain, range, inversef(x)f(x)f(x)f−1f^{-1}f−1Inverse graphReflection in the line y=xy = xy=x(a,b)(a,b)(a,b) becomes (b,a)(b,a)(b,a)Domain of f−1f^{-1}f−1 = range of fffRange of f−1f^{-1}f−1 = domain of fffWhen it existsNeeds one-to-one: horizontal line testNot one-to-one: same output from two inputsRestrict the domain to create an inverseReject solutions outside the restricted domainExam tipsf−1(x)f^{-1}(x)f−1(x) is not 1f(x)\frac{1}{f(x)}f(x)1Check inverse by substituting a value backDomain is about xxx, range about f(x)f(x)f(x)