11 The function f is such that \(\mathrm { f } ( x ) = 8 - ( x - 2 ) ^ { 2 }\), for \(x \in \mathbb { R }\).
- Find the coordinates and the nature of the stationary point on the curve \(y = \mathrm { f } ( x )\).
The function g is such that \(\mathrm { g } ( x ) = 8 - ( x - 2 ) ^ { 2 }\), for \(k \leqslant x \leqslant 4\), where \(k\) is a constant.
- State the smallest value of \(k\) for which g has an inverse.
For this value of \(k\),
- find an expression for \(\mathrm { g } ^ { - 1 } ( x )\),
- sketch, on the same diagram, the graphs of \(y = \mathrm { g } ( x )\) and \(y = \mathrm { g } ^ { - 1 } ( x )\).