(i)[3]
Rewrite $2x^2 - 12x + 13$ in the form $a(x + b)^2 + c$, where $a$, $b$ and $c$ are constants.
(ii)[1]
The function $f$ is given by $f(x) = 2x^2 - 12x + 13$ for $x \geq k$, where $k$ is a constant. It is stated that $f$ is one-one. State the smallest possible value of $k$.
(iii)[1]
The value of $k$ is now fixed as $7$. Find the range of $f$.
(iv)[5]
Find an expression for $f^{-1}(x)$ and state the domain of $f^{-1}$.