5 A function f is such that \(\mathrm { f } ( x ) = \frac { 15 } { 2 x + 3 }\) for \(0 \leqslant x \leqslant 6\).
- Find an expression for \(\mathrm { f } ^ { \prime } ( x )\) and use your result to explain why f has an inverse.
- Find an expression for \(\mathrm { f } ^ { - 1 } ( x )\), and state the domain and range of \(\mathrm { f } ^ { - 1 }\).