(i)[2]
Write $f(x)$ in the form $(x + a)^2 + b + k$, where $a$ and $b$ are constants.
(ii)[1]
State the range of $f$ in terms of $k$.
(iii)[1]
State the smallest value of $p$ for which $f$ is one-one.
(iv)[4]
Using the value of $p$ obtained in part (iii), determine an expression for $f^{-1}(x)$ and state the domain of $f^{-1}$, with both answers written in terms of $k$.