(i)[4]
Find the values of the constant $k$ for which the line $y + kx = 12$ is tangent to the curve $y = f(x)$.
(ii)[3]
Express $f(x)$ in the form $a(x + b)^2 + c$, with $a$, $b$ and $c$ as constants.
(iii)[1]
Find the range for $f$.
(iv)[1]
Find the least value of $A$ for which $g$ has an inverse, where $g : x \mapsto 2x^2 - 8x + 14$ is defined for $x > A$.
(v)[3]
For this value of $A$, find an expression for $g^{-1}(x)$ with $x$ as the variable.