Functions f and g are defined by

\(f : x \mapsto 4x - 2k\) for \(x \in \mathbb{R}\), where \(k\) is a constant,

\(g : x \mapsto \frac{9}{2-x}\) for \(x \in \mathbb{R}, x \neq 2\).

(i) Find the values of \(k\) for which the equation \(fg(x) = x\) has two equal roots. [4]

(ii) Determine the roots of the equation \(fg(x) = x\) for the values of \(k\) found in part (i). [3]