(i)[3]
Find the set of $p$ values for which the equation $f(x) = p$ has no real roots.
(ii)[3]
For $0 \leq x \leq 4$, the function $g$ is defined by $g: x \mapsto 2x^2 - 6x + 5$. Write $g(x)$ in the form $a(x + b)^2 + c$, where $a$, $b$ and $c$ are constants.
(iii)[2]
Find the range attained by $g$.
(iv)[1]
For $k \leq x \leq 4$, the function $h$ is defined by $h: x \mapsto 2x^2 - 6x + 5$, where $k$ is a constant. State the least value of $k$ for which $h$ has an inverse.
(v)[3]
For this value of $k$, give an expression for $h^{-1}(x)$.