Mathematics 9709 · AS & A Level · Functions

Functions — practice question

The functions $f$ and $g$ are defined so that $f(x) = x^2 + 3$ for $x > 0$, while $g(x) = 2x + 1$ for $x > -\frac{1}{2}$.

(a)[1]

Find a formula for $fg(x)$.

(b)[4]

Find a formula for $(fg)^{-1}(x)$, and state the domain of $(fg)^{-1}$.

(c)[4]

Solve for $x$ in the equation $fg(x) - 3 = gf(x)$.

Worked solution & mark scheme

This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Inverse correctly found: $f^{-1}(x)=(2x+1)^2+3$” …