Question 22
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 $x \geqslant -2$.
The function h is defined by $\mathrm{h}(x) = x - 2$ for $x \geqslant 0$.
**(f)** Explain why the composite function $\mathrm{h}\mathrm{g}^{-1}$ cannot be formed.
$\mathrm{f}(x) = \sqrt{x}$ for $x \geqslant 0$,
$\mathrm{g}(x) = 3\sqrt{x + 2} - 5$ for $x \geqslant -2$.
The function h is defined by $\mathrm{h}(x) = x - 2$ for $x \geqslant 0$.
**(f)** Explain why the composite function $\mathrm{h}\mathrm{g}^{-1}$ cannot be formed.
