10 Functions \(f\) and \(g\) are defined by
$$\begin{aligned}
& \mathrm { f } : x \mapsto 3 x - 4 , \quad x \in \mathbb { R } ,
& \mathrm {~g} : x \mapsto 2 ( x - 1 ) ^ { 3 } + 8 , \quad x > 1 .
\end{aligned}$$
- Evaluate fg(2).
- Sketch in a single diagram the graphs of \(y = \mathrm { f } ( x )\) and \(y = \mathrm { f } ^ { - 1 } ( x )\), making clear the relationship between the graphs.
- Obtain an expression for \(\mathrm { g } ^ { \prime } ( x )\) and use your answer to explain why g has an inverse.
- Express each of \(\mathrm { f } ^ { - 1 } ( x )\) and \(\mathrm { g } ^ { - 1 } ( x )\) in terms of \(x\).