CAIE IGCSE Mathematics Extended Finding Inverse Functions

Practise finding inverse functions by reversing a rule algebraically and using inverse notation to recover inputs or solve for unknown values.

Exam points

write y = f(x), interchange x and y and rearrange fully to state f⁻¹(x)
use f⁻¹(a) = b as equivalent to f(b) = a when solving for an unknown value
verify an inverse by checking that composition with the original function returns the input

[Maximum number: 2]

$10 \quad \mathrm{f}(x)=4-3 x \quad \mathrm{~g}(x)=x^{2}+x \quad \mathrm{~h}(x)=3^{x}$

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

$f^{-1}(x)=$

$\frac{4-x}{3}$ oe final answer.
M1 for x=4-3y, y+3x=4, x+3y=4, $\frac{y}{-3}=\frac{4}{-3}+x$ oe, or $\frac{x}{-3}=\frac{4}{-3}+y$ oe.

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