11 The equation of a curve is \(y = 8 x - x ^ { 2 }\).
- Express \(8 x - x ^ { 2 }\) in the form \(a - ( x + b ) ^ { 2 }\), stating the numerical values of \(a\) and \(b\).
- Hence, or otherwise, find the coordinates of the stationary point of the curve.
- Find the set of values of \(x\) for which \(y \geqslant - 20\).
The function g is defined by \(\mathrm { g } : x \mapsto 8 x - x ^ { 2 }\), for \(x \geqslant 4\).
- State the domain and range of \(\mathrm { g } ^ { - 1 }\).
- Find an expression, in terms of \(x\), for \(\mathrm { g } ^ { - 1 } ( x )\).