The diagram presents the graph of $y = f^{-1}(x)$, where $f^{-1}$ is given by $f^{-1}(x) = \frac{1 - 5x}{2x}$ for $0 < x \leq 2$.
(i)[5]
Find an expression for $f(x)$ and state the domain of $f$.
(ii)[2]
The function $g$ is defined by $g(x) = \frac{1}{x}$ for $x \geq 1$. Find an expression for $f^{-1}g(x)$, giving your answer in the form $ax + b$, where $a$ and $b$ are constants to determine.
Worked solution & mark scheme
This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Try to determine the inverse function” …