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