(i)[2]
Find the range for $f$.
(ii)[2]
Sketch the graph for $y = f(x)$.
(iii)[3]
Solve $f(x) = 6$, expressing your answers in terms of $\pi$.
(iv)[1]
The function $g$ is given by $g : x \mapsto 5 - 2\sin 2x$ for $0 \leq x \leq k$, where $k$ is a constant. State the greatest value of $k$ for which $g$ has an inverse.
(v)[3]
For this value of $k$, determine an expression for $g^{-1}(x)$.