Mathematics 9709 · AS & A Level · Functions

Functions — practice question

The functions $f$ and $g$ are given by $f(x) = \dfrac{2}{x^2 - 1}$ for $x < -1$, while $g(x) = x^2 + 1$ for $x > 0$.

(i)[3]

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

(ii)[4]

Solve the equation $g(f(x)) = 5$ for $x$.

Worked solution & mark scheme

This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Swaps $x,y$ to obtain $x^2=\frac{2}{y}+1$” …