Practice IB Mathematics Applications & Interpretation (AI) Topic AHL 2.7—composite Functions, Finding Inverse Function Incl Domain Restriction with authentic exam-style questions for both SL and HL students. This question bank focuses on the exact syllabus content for AHL 2.7—composite Functions, Finding Inverse Function Incl Domain Restriction and mirrors Paper 1, 2, 3 style where relevant.
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A calibration program converts every signed dimensionless reading by
(a) , explaining why both absence of overlap and absence of a range gap are required.
(b) For this value of , with correct branch domains.
The rule must be one-to-one and its outputs must include every real number.
For a circle of radius , , . Let .
(a) Evaluate .
(c) Solve the equation .
A signal-processing pipeline applies for input , then for . All values are dimensionless ratios to reference readings.
The function is defined by , .
(a) Write down the range of .
(b) Find an expression for .
(c) Write down the domain and range of .
A calibration pipeline applies , then , where inputs and responses are dimensionless real readings. The pipeline response is .
(b) an expression for .
(a) and , including their domains.
(b) , its domain and range, and hence find .
(c) Verify the inverse by composing in the correct order, then the unique for which .
(a) and , and verify one inverse identity for each.
(b) and find both directly and by composing the component inverses.
(c) A student proposes . both proposed inverse orders at and which one actually returns the input of .
