Functions f and g are defined by
$f:{\text{ }}x \mapsto 2{x^2} - 8x + 10$ for $0 \leqslant x \leqslant 2$,
$g:x \mapsto x$ for $0 \leqslant x \leqslant 10$.
a) Express $f\left( x \right)$ in the form $\alpha {\left( {x + b} \right)^2} + c$, where $\alpha $, $b$ and $c$ are constants.
b) State the range of $f$.
c) State the domain of ${f^{ - 1}}$.
d) ketch on the same diagram the graphs of $y = f\left( x \right)$, $y = g\left( x \right)$ and $y = {f^{ - 1}}\left( x \right)$, making clear the relationship between the graphs.
e) Find an expression for ${f^{ - 1}}\left( x \right)$.
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