11 Functions \(f\) and \(g\) are defined by
$$\begin{array} { l l }
\mathrm { f } : x \mapsto 2 x ^ { 2 } - 8 x + 10 & \text { for } 0 \leqslant x \leqslant 2
\mathrm {~g} : x \mapsto x & \text { for } 0 \leqslant x \leqslant 10
\end{array}$$
- Express \(\mathrm { f } ( x )\) in the form \(a ( x + b ) ^ { 2 } + c\), where \(a , b\) and \(c\) are constants.
- State the range of f .
- State the domain of \(\mathrm { f } ^ { - 1 }\).
- Sketch on the same diagram the graphs of \(y = \mathrm { f } ( x ) , y = \mathrm { g } ( x )\) and \(y = \mathrm { f } ^ { - 1 } ( x )\), making clear the relationship between the graphs.
- Find an expression for \(\mathrm { f } ^ { - 1 } ( x )\).