Mathematics 9709 · AS & A Level · Functions

Functions — practice question

The mapping $f$ is defined as $f : x \mapsto \dfrac{2}{3 - 2x}$ for $x \in \mathbb{R}$, $x \neq \dfrac{3}{2}$.

(i)[3]

Find a formula for $f^{-1}(x)$.

(ii)[3]

Determine the value of $a$ such that $gf(-1) = 3.$

(iii)[4]

Find the possible values of $a$ if the equation $f^{-1}(x) = g^{-1}(x)$ has two equal roots.

Worked solution & mark scheme

This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Make $x$ the subject in $y=\dfrac{2}{3-2x}$” …