Functions f, g and h are defined for \(x \in \mathbb{R}\) by

\(f(x) = 3 \cos 2x + 2\),

\(g(x) = f(2x) + 4\),

\(h(x) = 2f\left(x + \frac{1}{2}\pi\right)\).

(d) Describe fully a sequence of transformations that maps the graph of \(y = f(x)\) on to \(y = g(x)\). [2]

(e) Describe fully a sequence of transformations that maps the graph of \(y = f(x)\) on to \(y = h(x)\). [2]