Mathematics 9709 · AS & A Level · Functions

Functions — practice question

The functions $f$ and $g$ are specified by $f : x \mapsto \dfrac{3}{2x + 1}$ for $x > 0$, $g : x \mapsto \dfrac{1}{x} + 2$ for $x > 0$.

(i)[3]

Find the range of $f$, and also the range of $g$.

(ii)[2]

Find an expression for $fg(x)$, and give your answer in the form $\frac{ax}{bx+c}$, where $a$, $b$ and $c$ are integers.

(iii)[3]

Find an expression for $(fg)^{-1}(x)$, giving your answer in the same style as part (ii).

Worked solution & mark scheme

This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “The range of $f$ satisfies $0<f(x)<3$” …