Mathematics 9709 · AS & A Level · Functions

Functions — practice question

The function $f$ is specified by $f(x) = -3x^2 + 2$ for $x \leq -1$.

(a)[1]

State the range for $f$.

(b)[3]

Find an expression for the inverse function $f^{-1}(x)$.

(c)[5]

The function $g$ is specified by $g(x) = -x^2 - 1$ for $x \leq -1$. Solve the equation $fg(x) - gf(x) + 8 = 0$.

Worked solution & mark scheme

This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “State the range as $y\le -1$.” …