8 The functions f and g are defined for \(x \geqslant 0\) by
$$\begin{aligned}
& \mathrm { f } : x \mapsto 2 x ^ { 2 } + 3
& \mathrm {~g} : x \mapsto 3 x + 2
\end{aligned}$$
- Show that \(\operatorname { gf } ( x ) = 6 x ^ { 2 } + 11\) and obtain an unsimplified expression for \(\operatorname { fg } ( x )\).
- Find an expression for \(( \mathrm { fg } ) ^ { - 1 } ( x )\) and determine the domain of \(( \mathrm { fg } ) ^ { - 1 }\).
- Solve the equation \(\mathrm { gf } ( 2 x ) = \mathrm { fg } ( x )\).