10 A function f is defined by \(\mathrm { f } : x \mapsto 5 - 2 \sin 2 x\) for \(0 \leqslant x \leqslant \pi\).
- Find the range of f .
- Sketch the graph of \(y = \mathrm { f } ( x )\).
- Solve the equation \(\mathrm { f } ( x ) = 6\), giving answers in terms of \(\pi\).
The function g is defined by \(\mathrm { g } : x \mapsto 5 - 2 \sin 2 x\) for \(0 \leqslant x \leqslant k\), where \(k\) is a constant.
- State the largest value of \(k\) for which g has an inverse.
- For this value of \(k\), find an expression for \(\mathrm { g } ^ { - 1 } ( x )\).