CAIE IGCSE Mathematics Extended E2.13.2 Understand and Find Inverse Functions F 1 X Questions

Practise Extended CAIE IGCSE Mathematics by rearranging functions, checking inverses and interpreting inverse graphs.

Exam points

Understand the meaning of an inverse function and its notation f⁻¹(x).
Find an inverse function using algebraic rearrangement and verify the result.
Use graphs or mappings to interpret the relationship between a function and its inverse.

[Maximum number: 3]

\mathrm{f}(x)=5^{x} \quad \mathrm{~g}(x)=3 x-2 \quad \mathrm{~h}(x)=x^{2}+1

(a)

Find $\mathrm{g}^{-1}(x)$ .

\mathrm{g}^{-1}(x)=

[ 2 ]

$\frac{x+2}{3}$ or $\frac{x}{3}+\frac{2}{3}$ final answer

M1 for correct first step
e.g. x=3 y-2 or y+2=3 x or $\frac{y}{3}=x-\frac{2}{3}$
oe

(b)

Find $\mathrm{ff}^{-1}(12)$ .

[ 1 ]

All question bank results loaded