8 The functions f and g are defined as follows, where \(a\) and \(b\) are constants.
$$\begin{aligned}
& \mathrm { f } ( x ) = 1 + \frac { 2 a } { x - a } \text { for } x > a
& \mathrm {~g} ( x ) = b x - 2 \text { for } x \in \mathbb { R }
\end{aligned}$$
- Given that \(\mathrm { f } ( 7 ) = \frac { 5 } { 2 }\) and \(\mathrm { gf } ( 5 ) = 4\), find the values of \(a\) and \(b\).
For the rest of this question, you should use the value of \(a\) which you found in (a). - Find the domain of \(\mathrm { f } ^ { - 1 }\).
- Find an expression for \(\mathrm { f } ^ { - 1 } ( x )\).