5 The function f is defined by
$$\mathrm { f } ( x ) = 16 x - \mathrm { e } ^ { 2 x } , \text { for all real } x$$
The graph of \(y = \mathrm { f } ( x )\) is sketched below.
\includegraphics[max width=\textwidth, alt={}, center]{bf427498-f1ee-4167-a6f2-ddaa2ff5ef81-12_789_1349_534_347}
- Find the range of f.
- The composite function fg is defined by
$$\operatorname { fg } ( x ) = \frac { 16 } { x } - \mathrm { e } ^ { \frac { 2 } { x } } , \text { for real } x , x \neq 0$$
Find an expression for \(\operatorname { gg } ( x )\).