Mathematics 9709 · AS & A Level · Functions

Functions — practice question

The function $f$ is given by $f : x \mapsto \frac{x + 3}{2x - 1}$, $x \in \mathbb{R}$, $x \neq \tfrac{1}{2}$.

(i)[3]

Show that the composition $ff(x) = x$.

(ii)[2]

Hence, or otherwise, obtain the inverse function $f^{-1}(x)$.

Worked solution & mark scheme

This 5-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Substitution of $f(x)$ into the function itself” …