8 A function f is defined by \(\mathrm { f } : x \mapsto ( 2 x - 3 ) ^ { 3 } - 8\), for \(2 \leqslant x \leqslant 4\).
- Find an expression, in terms of \(x\), for \(\mathrm { f } ^ { \prime } ( x )\) and show that f is an increasing function.
- Find an expression, in terms of \(x\), for \(\mathrm { f } ^ { - 1 } ( x )\) and find the domain of \(\mathrm { f } ^ { - 1 }\).