The function f is defined by
$f\left( x \right) = {x^2} - 4x + 7$ for $x \gt 2$.
a) Express $f\left( x \right)$ in the form ${\left( {x - \alpha } \right)^2} + b$ and hence state the range of f.
b) Obtain an expression for ${f^{ - 1}}\left( x \right)$ and state the domain of ${f^{ - 1}}$
The function g is defined by
$g\left( x \right) = x - 2{\text{ }}$ for $x \gt 2$.
The function h is such that $f = hg$ and the domain of $h$ is $x \gt 0$.
c) Obtain an expression for $h\left( x \right)$.
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