The functions f and g are defined for \(x > 0\) by

\(f : x \mapsto 2x^2 + 3\),

\(g : x \mapsto 3x + 2\).

(i) Show that \(gf(x) = 6x^2 + 11\) and obtain an unsimplified expression for \(fg(x)\). [2]

(ii) Find an expression for \((fg)^{-1}(x)\) and determine the domain of \((fg)^{-1}\). [5]

(iii) Solve the equation \(gf(2x) = fg(x)\). [3]