8 A function f is defined by \(\mathrm { f } : x \mapsto 3 \cos x - 2\) for \(0 \leqslant x \leqslant 2 \pi\).
- Solve the equation \(\mathrm { f } ( x ) = 0\).
- Find the range of f .
- Sketch the graph of \(y = \mathrm { f } ( x )\).
A function g is defined by \(\mathrm { g } : x \mapsto 3 \cos x - 2\) for \(0 \leqslant x \leqslant k\).
- State the maximum value of \(k\) for which g has an inverse.
- Obtain an expression for \(\mathrm { g } ^ { - 1 } ( x )\).