11 The function f : \(x \mapsto 4 - 3 \sin x\) is defined for the domain \(0 \leqslant x \leqslant 2 \pi\).
- Solve the equation \(\mathrm { f } ( x ) = 2\).
- Sketch the graph of \(y = \mathrm { f } ( x )\).
- Find the set of values of \(k\) for which the equation \(\mathrm { f } ( x ) = k\) has no solution.
The function \(\mathrm { g } : x \mapsto 4 - 3 \sin x\) is defined for the domain \(\frac { 1 } { 2 } \pi \leqslant x \leqslant A\).
- State the largest value of \(A\) for which g has an inverse.
- For this value of \(A\), find the value of \(\mathrm { g } ^ { - 1 } ( 3 )\).
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