(a)[2]
On the diagram above, sketch $y = f^{-1}(x)$.
(b)[2]
Find a formula for $f^{-1}(x)$.
(c)[2]
The diagram above shows part of the graph of $g(x)=3+2\sin\left(\tfrac{1}{4}x\right)$ for $-2\pi\le x\le 2\pi$. Complete the sketch of $g(x)$ on the diagram above and hence explain whether the function $g$ has an inverse.
(d)[6]
Describe fully a sequence of three transformations that may be combined to change the graph of $y=\sin x$ for $0\le x\le \tfrac{1}{2}\pi$ into the graph of $y=f(x)$, making the order of application clear.