Cambridge AS & A Level. 2025. Mathematics (9709). May/June - Paper 1 (11) · Pure Mathematics 1 - Question 19

The functions f and g are defined by

$\mathrm{f}(x) = \sqrt{x}$ for $x \geqslant 0$,

$\mathrm{g}(x) = 3\sqrt{x + 2} - 5$ for $x \geqslant -2$.

**(c)** Find an expression for $\mathrm{g}^{-1}(x)$.