IB Maths AI SL 2.2 Functions and inverses Question Bank

Practise IB Maths AI SL 2.2 through questions on evaluating functions, inverse notation, compositions and interpreting models.

Exam points

Evaluate functions and compositions accurately from formulae, tables, graphs or stated inputs.
Find or use an inverse function and explain the meaning of its input and output in context.
Check domain, range and substitution by composing the function with its proposed inverse.

[Maximum number: 6]

A function is defined by $f(x)=\frac{4}{x}-3$ , for $-6 \leq x \leq 10, x \neq 0$ .

(a)

Find f(10).

[ 1 ]

$-2.6\left(\frac{-13}{5}\right)$

(b)

Find the range of f.

[ 3 ]

EITHER
$(-\infty,-3.67] \cup[-2.6, \infty)$
A1A1A1
OR
$y \leq-3.67$ or $y \geq-2.6$
A1A1A1

Note: Award A1 for $-3.67\left(-3.66666 \ldots,-\frac{11}{3}\right)$ seen
A1 for their $-2.6\left(-\frac{13}{5}\right)$ seen and both sets of inequalities/brackets correct;
A1 if completely correct, including union symbol or "or".
It is possible to award A0A1A0 for correctly presenting their -3.67 (and their -2.6 ).
The -3.67 maybe seen as part of a sketch.

Award A1A0A0 for $-3.67 \leq y \leq-2.6$ or [-3.67,-2.6].

(c)

Find $f^{-1}(-2)$ .

[ 2 ]

setting f(x) equal to -2 f(x)=-2 OR $-2=\frac{4}{x}-3$ OR sketch of graph with line labelled -2

All question bank results loaded

SL 2.2—Functions and inverses question 1

Question (a)

Question (b)

Question (c)