Mathematics 9709 · AS & A Level · Functions

Functions — practice question

Functions $f$ and $g$ are defined on $x \in \mathbb{R}$ by $f : x \mapsto 2x + 1$, $g : x \mapsto x^2 - 2$.
(i)[2]

Find simplified expressions for $fg(x)$ and $gf(x)$.

(ii)[3]

Find the value of $a$ such that $fg(a) = gf(a)$.

(iii)[2]

Find the value of $b$ $(b \neq a)$ satisfying $g(b) = b$.

(iv)[2]

Find a simplified expression for $f^{-1}g(x)$.

(v)[2]

Find an expression for $h^{-1}(x)$, where $h : x \mapsto x^2 - 2$, when $x \leq 0$.

Worked solution & mark scheme

This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: Derives $fg(x)=2x^2-3$

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