8 The function f : \(x \mapsto 5 + 3 \cos \left( \frac { 1 } { 2 } x \right)\) is defined for \(0 \leqslant x \leqslant 2 \pi\).
- Solve the equation \(\mathrm { f } ( x ) = 7\), giving your answer correct to 2 decimal places.
- Sketch the graph of \(y = \mathrm { f } ( x )\).
- Explain why f has an inverse.
- Obtain an expression for \(\mathrm { f } ^ { - 1 } ( x )\).