Question 21
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 $x \geqslant 0$.
(In part (c) you found $\mathrm{g}^{-1}(x) = \left(\dfrac{x + 5}{3}\right)^2 - 2$.)
**(e)** Find the value of $\mathrm{g}^{-1}\mathrm{h}(4)$.
$\mathrm{f}(x) = \sqrt{x}$ 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 $x \geqslant 0$.
(In part (c) you found $\mathrm{g}^{-1}(x) = \left(\dfrac{x + 5}{3}\right)^2 - 2$.)
**(e)** Find the value of $\mathrm{g}^{-1}\mathrm{h}(4)$.
