CAIE A-Level Mathematics AS 1.2.1 Function Terminology Questions

Practise using function, domain, range, one-to-one, inverse and composition notation to evaluate values, solve input equations and state inverse restrictions correctly.

Exam points

use function notation correctly
determine domains and ranges
evaluate and interpret composite functions

[Maximum number: 2]

Functions f and g are defined by

\begin{aligned} & \mathrm{f}(x)=(x+a)^{2}-a \text { for } x \leqslant-a, \\ & \mathrm{~g}(x)=2 x-1 \text { for } x \in \mathbb{R}, \end{aligned}

where a is a positive constant.

(a)

State the domain of the function $\mathrm{f}^{-1}$ .

[ 1 ]

$x \geqslant-a$
Marking guidance:

Ignore infinity limit if included.

(b)

State the range of the function $\mathrm{f}^{-1}$ .

[ 1 ]

y or $f^{-1}[(x)] \leqslant-a$
Marking guidance:

Ignore negative infinity limit if included.

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CAIE A-Level Mathematics AS 1.2.1 Function Terminology Questions question 1

Question (a)

Question (b)