9 The function f is defined by \(\mathrm { f } ( x ) = 2 - 3 \cos x\) for \(0 \leqslant x \leqslant 2 \pi\).
- State the range of f .
- Sketch the graph of \(y = \mathrm { f } ( x )\).
The function g is defined by \(\mathrm { g } ( x ) = 2 - 3 \cos x\) for \(0 \leqslant x \leqslant p\), where \(p\) is a constant.
- State the largest value of \(p\) for which g has an inverse.
- For this value of \(p\), find an expression for \(\mathrm { g } ^ { - 1 } ( x )\).