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: 4]

$f(x)=3-2x\qquad g(x)=2x+3\qquad h(x)=2^x$

(a)

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

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

[ 2 ]

$\frac{3-x}{2}$ oe final answer

M1 for y+2x=3, for $\frac{y}{2}=\frac32-x$ , or for x=3-2y.

(b)

Find x when $\mathrm{h}^{-1}(x)=5$ .

[ 2 ]

32

2

M1 for $[x=] \mathrm{h}(5)$

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