(i)[2]
Express the quadratic $x^2 - 4x + 7$ in the form $(x + a)^2 + b$.
(ii)[1]
The function $f$ is given by $f(x) = x^2 - 4x + 7$ for $x < k$, where $k$ is a constant. State the greatest value of $k$ for which $f$ is a decreasing function.
(iii)[3]
The value of $k$ is now $1$. Find an expression for $f^{-1}(x)$ and state the domain of $f^{-1}$.
(iv)[4]
The function $g$ is defined by $g(x) = \frac{2}{x - 1}$ for $x > 1$. Find an expression for $gf(x)$ and state the range of $gf$.