Mathematics 9709 · AS & A Level · Functions

Functions — practice question

Functions $f$ and $g$ are given by: $f: x \mapsto x^2 + 2x + 3$ when $x \leq -1$, $g: x \mapsto 2x + 1$ when $x \geq -1$.

(a)[3]

Express $f(x)$ as $(x + a)^2 + b$, then state the range of $f$.

(b)[2]

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

(c)[3]

Solve $gf(x) = 13$.

Worked solution & mark scheme

This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Correctly written form: $f(x) = (x+1)^2 + 2$” …