IB Maths AI HL 2.2 Functions and inverses Question Bank

Practise IB Maths AI HL 2.2 through questions that extend functions to parameters, inverse models, compositions and domain-range decisions.

Exam points

Solve HL inverse and composition problems with parameters and restricted domains.
Use a function model to connect inputs, outputs and inverse interpretations in a multi-step context.
Justify domain and range restrictions and verify the inverse by composition or graphical reasoning.

[Maximum number: 2]

The function f is defined by $f(x)=4 \ln (2 x-3)$ , where $x>\frac{3}{2}$ .
The graph of y=f(x) is obtained from the graph of $y=\ln x$ by a sequence of three transformations.

The graph of y=g(x) is shown.
The graph passes through the points (-2,-2),(-1,0),(0,2),(1,3),(2,5) and (3,6).

Figure for Question SL 2.2—Functions and inverses question 1 — IB Maths AI HL

Find $(f \circ g)(2)$ .

$\quad g(2)=5$ $f(5)=7.78 \quad(=7.78364 \ldots, 4 \ln 7)$

All question bank results loaded

SL 2.2—Functions and inverses question 1