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IB Maths AA HL 2.5 Composite, inverse and restricted functions Question Bank

Practise IB Maths AA HL 2.5 by analysing composite and inverse functions with domain restrictions and multiple possible mappings.

Syllabus
First assessment 2021
Course
Mathematics: analysis and approaches HL
Level
HL

Exam points

  • Derive a composite or inverse function while tracking domain and range restrictions.
  • Solve a function equation with multiple possible mappings and reject invalid branches.
  • Use symmetry, intersections and algebraic constraints to evaluate a function/inverse relationship.

SL 2.5—Composite and inverse functions question 1

[Maximum number: 5]

Consider the function f(x)=ax3+bx2+cx+df(x)=a x^{3}+b x^{2}+c x+d, where x∈Rx \in \mathbb{R} and a,b,c,d∈Ra, b, c, d \in \mathbb{R}.

Sketch the graphs of y=g(x) and y=g−1(x)y=g^{-1}(x) on the same set of axes, indicating the points where each graph crosses the coordinate axes.

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