The function $f$ is given by $f : x \mapsto 2x + k$, $x \in \mathbb{R}$, where $k$ is a fixed constant.
(i)[2]
For $k = 3$, solve the equation $f(f(x)) = 25$.
(ii)[3]
The function $g$ is given by $g : x \mapsto x^2 - 6x + 8$, $x \in \mathbb{R}$. Determine the set of values of $k$ for which the equation $f(x) = g(x)$ has no real solutions.
(iii)[4]
The function $h$ is given by $h : x \mapsto x^2 - 6x + 8$, $x > 3$. Find an expression for $h^{-1}(x)$.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Constructs $f(f(x))$ correctly” …