8 Functions f and g are defined by
$$\begin{array} { l l }
\mathrm { f } : x \mapsto 4 x - 2 k & \text { for } x \in \mathbb { R } , \text { where } k \text { is a constant, }
\mathrm { g } : x \mapsto \frac { 9 } { 2 - x } & \text { for } x \in \mathbb { R } , x \neq 2 .
\end{array}$$
- Find the values of \(k\) for which the equation \(\mathrm { fg } ( x ) = x\) has two equal roots.
- Determine the roots of the equation \(\operatorname { fg } ( x ) = x\) for the values of \(k\) found in part (i).