(i)[3]
Write $2x^2 - 12x + 11$ in the form $a(x + b)^2 + c$, with $a$, $b$ and $c$ as constants.
(ii)[1]
The function $f$ is given by $f(x) = 2x^2 - 12x + 11$ for $x \le k$. State the greatest value of the constant $k$ that makes $f$ a one-one function.
(iii)[4]
For this value of $k$, find an expression for $f^{-1}(x)$ and state the domain of $f^{-1}$.
(iv)[3]
The function $g$ is defined by $g(x) = x + 3$ for $x \le p$. With $k$ now equal to $1$, find the largest value of the constant $p$ that permits the composite function $fg$ to be formed, and determine an expression for $fg(x)$ whenever this composite function exists.