The function $f$ is given by $f(x) = 8 - (x - 2)^2$, for $x \in \mathbb{R}$. The function $g$ is given by $g(x) = 8 - (x - 2)^2$, for $k \leq x \leq 4$, where $k$ is a constant.
(i)[3]
Find the coordinates of the stationary point on the curve $y = f(x)$ and state its nature.
(ii)[1]
State the least value of $k$ for which $g$ has an inverse.
(iii)[3]
For this value of $k$, find an expression for $g^{-1}(x)$.
(iv)[3]
Sketch, on the same diagram, the graphs of $y = g(x)$ and $y = g^{-1}(x)$.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Stationary point at $x=2$.” …