5 The function f is defined by \(\mathrm { f } ( x ) = - 2 x ^ { 2 } + 12 x - 3\) for \(x \in \mathbb { R }\).
- Express \(- 2 x ^ { 2 } + 12 x - 3\) in the form \(- 2 ( x + a ) ^ { 2 } + b\), where \(a\) and \(b\) are constants.
- State the greatest value of \(\mathrm { f } ( x )\).
The function g is defined by \(\mathrm { g } ( x ) = 2 x + 5\) for \(x \in \mathbb { R }\). - Find the values of \(x\) for which \(\operatorname { gf } ( x ) + 1 = 0\).