CAIE IGCSE Additional Math 1.6 find inverse functions

Use this inverse-functions page to rearrange function rules, write f⁻¹(x) and include the domain restrictions that make the inverse valid.

Exam points

Rearrange a function rule to find an expression for the inverse function.
State the inverse function's domain when the original function has restrictions.
Show inverse results involving square roots or rational expressions in simplest form.

[Maximum number: 4]

A function g is defined by $g(x)=e^{\sqrt{x-2}}$ for $x\geqslant 2$ .

Find an expression for $g^{-1}(x)$ .

Complete method including change of subject and swap of variables at some point.
M2; M1 for $\ln y=\sqrt{x-2}$ or $\ln x=\sqrt{y-2}$ soi
$g^{-1}(x)=(\ln x)^2+2$
A1 Final answer

All question bank results loaded

1.6. Find inverse functions question 1