9 The function f is defined by \(\mathrm { f } : x \mapsto 2 x ^ { 2 } - 12 x + 7\) for \(x \in \mathbb { R }\).
- Express \(\mathrm { f } ( x )\) in the form \(a ( x - b ) ^ { 2 } - c\).
- State the range of f .
- Find the set of values of \(x\) for which \(\mathrm { f } ( x ) < 21\).
The function g is defined by \(\mathrm { g } : x \mapsto 2 x + k\) for \(x \in \mathbb { R }\).
- Find the value of the constant \(k\) for which the equation \(\operatorname { gf } ( x ) = 0\) has two equal roots.