Mathematics 9709 · AS & A Level · Functions

Functions — practice question

The functions $f$ and $g$ are given by $f: x \mapsto 2x^2 - 8x + 10$ for $0 \leq x \leq 2$, and $g: x \mapsto x$ for $0 \leq x \leq 10$.
(i)[3]

Write $f(x)$ in the form $a(x + b)^2 + c$, where $a$, $b$ and $c$ are constants.

(ii)[1]

State the range for $f$.

(iii)[1]

State the domain for $f^{-1}$.

(iv)[4]

On the same diagram, sketch the graphs of $y = f(x)$, $y = g(x)$ and $y = f^{-1}(x)$, showing clearly how the graphs are related.

(v)[3]

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

Worked solution & mark scheme

This 12-mark question has a full step-by-step worked solution and mark scheme. One marking point: Correct expression $2(x-2)^2+2$

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