CAIE IGCSE Additional Math 1.6 Find Inverse Functions Questions

Practise Cambridge IGCSE Additional Mathematics by rearranging function equations, selecting valid inverse branches and stating inverse domains and ranges.

Exam points

Find inverse functions algebraically by interchanging variables and solving for the original input.
Use correct inverse-function notation and state the domain and range of the inverse where required.
Select the correct branch or restriction so the inverse corresponds to the original one-one function.

[Maximum number: 2]

It is given that $\mathrm{f}(x)=2 \ln (3 x-4)$ , for x>a, and that $\mathrm{f}^{-1}$ exists.

For your value of a, find an expression for $\mathrm{f}^{-1}(x)$ .

$\left[\mathrm{f}^{-1}(x)\right]=\frac{4+\mathrm{e}^{\frac{x}{2}}}{3}$ oe

M1 for a complete valid method,
allow a sign error
A1 must be using the correct notation

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CAIE IGCSE Additional Math 1.6 Find Inverse Functions Questions question 1