CAIE A-Level Mathematics 1.2.1 Function Terminology

CAIE A-Level Mathematics 1.2.1 Function Terminology
Cambridge International AS & A Level Mathematics 9709 syllabus for exams in 2028, 2029 and 20302028–2030

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

How this is tested

  • substitute an input into f or solve f(a) = k while preserving brackets and restrictions
  • state the domain or range of an inverse using the correct variable and endpoint inequality
  • distinguish one-to-one and inverse notation from reciprocal or ordinary algebraic notation

Question 8

[Maximum number: 2]

Functions f and g are defined by

f(x)=(x+a)2−a for x⩽−a, g(x)=2x−1 for x∈R,\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.

Question 8(b)(i)

(a)

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

[ 1 ]

Question 8(b)(ii)

(b)

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

[ 1 ]