IB Maths AA HL 2.2 Functions and inverses Question Bank

Practise IB Maths AA HL 2.2 through questions that extend functions to parameters, inverse models, compositions and restricted domains.

Exam points

Solve HL inverse and composition problems with parameters and carefully stated restrictions.
Use a function model to connect inputs, outputs and inverse interpretations in multi-step contexts.
Justify domain and range choices and verify the inverse algebraically or graphically.

[Maximum number: 1]

A function f is defined by $f(x)=\arcsin \left(\frac{x^{2}-1}{x^{2}+1}\right), x \in \mathbb{R}$ .

State the domain of $g^{-1}$ .

domain is $-\frac{\pi}{2} \leq x<\frac{\pi}{2}$
Note: Accept correct alternative notations, for example, $\left\lfloor-\frac{\pi}{2}, \frac{\pi}{2}\right\rfloor$ or $\left\lfloor-\frac{\pi}{2}, \frac{\pi}{2}\right)$ .

Marking guidance:

Accept [-1.57,1.57[ if correct to 3 s.f.

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SL 2.2—Functions and inverses question 1