10 The function f is defined by \(\mathrm { f } : x \mapsto 2 x ^ { 2 } - 12 x + 13\) for \(0 \leqslant x \leqslant A\), where \(A\) is a constant.
- Express \(\mathrm { f } ( x )\) in the form \(a ( x + b ) ^ { 2 } + c\), where \(a , b\) and \(c\) are constants.
- State the value of \(A\) for which the graph of \(y = \mathrm { f } ( x )\) has a line of symmetry.
- When \(A\) has this value, find the range of f .
The function g is defined by \(\mathrm { g } : x \mapsto 2 x ^ { 2 } - 12 x + 13\) for \(x \geqslant 4\).
- Explain why \(g\) has an inverse.
- Obtain an expression, in terms of \(x\), for \(\mathrm { g } ^ { - 1 } ( x )\).