Mathematics 9709 · AS & A Level · Functions

Functions — practice question

For $x \geq 0$, the functions $f$ and $g$ are given by $f : x \mapsto 2x^2 + 3$ and $g : x \mapsto 3x + 2$.

(i)[2]

Show that $gf(x)=6x^2+11$ and give an unsimplified form for $fg(x)$.

(ii)[5]

Find an expression for $(fg)^{-1}(x)$ and state the domain of $(fg)^{-1}$.

(iii)[3]

Solve the equation formed by setting $gf(2x)=fg(x)$.

Worked solution & mark scheme

This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Find $gf(x)$, giving $3(2x^2+3)+2=6x^2+11$.” …