(a)[3]
Find the set of $x$ values for which $f(x) \le 3$.
(b)[3]
Given that $y = mx + c$ is tangent to the curve $y = f(x)$, show that $4c = m^2 - 12m + 16$.
(c)[2]
The function $g$ is defined by $g : x \mapsto 6x - x^2 - 5$ for $x \ge k$, where $k$ is a constant. Write $6x - x^2 - 5$ in the form $a - (x - b)^2$, with $a$ and $b$ as constants.
(d)[1]
State the least value of $k$ for which $g$ has an inverse.
(e)[2]
For this value of $k$, find an expression for $g^{-1}(x)$.