(i)[2]
Express $7 - 2x^2 - 12x$ in the form $a - 2(x + b)^2$, with $a$ and $b$ as constants.
(ii)[1]
State the coordinates of the stationary point that lies on the curve $y = f(x)$.
(iii)[1]
The function $g$ is defined by $g : x \mapsto 7 - 2x^2 - 12x$ for $x \geq k$. State the least value of $k$ that allows $g$ to have an inverse.
(iv)[3]
For this value of $k$, determine $g^{-1}(x)$.