(a)[5]
Describe the complete sequence of transformations that carries the graph of $y=f(x)$ to the graph of $y=g(x)$. Make the order in which they are applied clear.
(b)[2]
On the diagram sketch the graph of $y=g^{-1}(x)$ and any relevant mirror line.
(c)[2]
Find a formula for $g^{-1}(x)$.
(d)[1]
State the range for $g^{-1}$.
(e)[1]
The function $h$ is defined for $x \geq 0$ by $h(x) = x - 2$. Find the value of $g^{-1}h(4)$.
(f)[1]
Explain why the composite function $hg^{-1}$ is impossible to define.