7 A function f is defined by f : \(x \mapsto 3 - 2 \tan \left( \frac { 1 } { 2 } x \right)\) for \(0 \leqslant x < \pi\).
- State the range of f .
- State the exact value of \(\mathrm { f } \left( \frac { 2 } { 3 } \pi \right)\).
- Sketch the graph of \(y = \mathrm { f } ( x )\).
- Obtain an expression, in terms of \(x\), for \(\mathrm { f } ^ { - 1 } ( x )\).