7 The function f is defined by \(\mathrm { f } : x \mapsto 7 - 2 x ^ { 2 } - 12 x\) for \(x \in \mathbb { R }\).
- Express \(7 - 2 x ^ { 2 } - 12 x\) in the form \(a - 2 ( x + b ) ^ { 2 }\), where \(a\) and \(b\) are constants.
- State the coordinates of the stationary point on the curve \(y = \mathrm { f } ( x )\).
The function g is defined by \(\mathrm { g } : x \mapsto 7 - 2 x ^ { 2 } - 12 x\) for \(x \geqslant k\). - State the smallest value of \(k\) for which g has an inverse.
- For this value of \(k\), find \(\mathrm { g } ^ { - 1 } ( x )\).