9 The function f is defined by \(\mathrm { f } : x \mapsto 2 x ^ { 2 } - 12 x + 7\) for \(x \in \mathbb { R }\).
- Express \(2 x ^ { 2 } - 12 x + 7\) in the form \(2 ( x + a ) ^ { 2 } + b\), where \(a\) and \(b\) are constants.
- State the range of f .
The function g is defined by \(\mathrm { g } : x \mapsto 2 x ^ { 2 } - 12 x + 7\) for \(x \leqslant k\). - State the largest value of \(k\) for which g has an inverse.
- Given that g has an inverse, find an expression for \(\mathrm { g } ^ { - 1 } ( x )\).