(a)[3]
Write $f(x)$ in the form $a - b(x - c)^2$, where $a$, $b$ and $c$ are constants, and state the range of $f$.
(b)[2]
A reflection in one of the axes, followed by a translation, takes the graph of $y = f(x)$ to the graph of $y = h(x)$. It is given that the graph of $y = h(x)$ has a minimum point at the origin. Give details of the reflection and translation involved.
(c)[2]
Sketch the graph of $y = g(x)$ and explain why $g$ is a one-one function. You do not need to determine the coordinates of any intersections with the axes.
(d)[4]
Sketch the graph of $y = g^{-1}(x)$ on your diagram in (c), and find an expression for $g^{-1}(x)$. You should label the two graphs in your diagram appropriately and show any relevant mirror line.