- The functions \(f\) and \(g\) are defined with their respective domains by
$$\begin{array} { l l }
\mathrm { f } ( x ) = x ^ { 2 } - 6 x + 5 , & \text { for } x \geqslant 3
\mathrm {~g} ( x ) = | x - 6 | , & \text { for all real values of } x
\end{array}$$
- Find the range of f .
- The inverse of f is \(\mathrm { f } ^ { - 1 }\).
Find \(\mathrm { f } ^ { - 1 } ( x )\). Give your answer in its simplest form.
- Find \(\mathrm { gf } ( x )\).
- Solve the equation \(\operatorname { gf } ( x ) = 6\).