(a)[2]
Write $2x^2 + 12x + 11$ in the form $2(x + a)^2 + b$, where $a$ and $b$ are constants.
(b)[3]
The function $f$ is given by $f(x) = 2x^2 + 12x + 11$ for $x \leq -4$. Find an expression for $f^{-1}(x)$ and give the domain of $f^{-1}$.
(c)[2]
When $k = -1$, solve the equation $fg(x) = 193$.
(d)[1]
State the largest possible value of $k$ for the composition $fg$ to be defined.