IB Maths AI SL 2.2 Functions and Inverses Questions

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

Exam points

Evaluate and compose functions from formulae, tables, graphs or contexts, keeping the input and output roles clear.
Find or use an inverse function, including the restriction needed for a one-to-one function.
Use inverse and composite functions in a model, and verify the result by composition, domain/range or graph reflection.

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Study SL 2.2—Functions and inverses conceptsOpen the corresponding Concept lesson for explanations, examples and exam connections.

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

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IB Maths AI SL 2.2 Functions and Inverses Questions question 1

Question (a)

Question (b)

Question (c)