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Date	May 2017	Marks available	3	Reference code	17M.1.sl.TZ1.2
Level	SL only	Paper	1	Time zone	TZ1
Command term	Find	Question number	2	Adapted from	N/A

Question

Let $f(x) = 5x$ and $g(x) = {x^2} + 1$ , for $x \in \mathbb{R}$ .

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

[2]

Find $(f \circ g)(7)$ .

[3]

Markscheme

interchanging $x$ and $x$ (M1)

eg $\,\,\,\,\,$ $x = 5y$

${f^{ - 1}}\left( x \right) = \frac{x}{5}$ A1 N2

[2 marks]

METHOD 1

attempt to substitute 7 into $g(x)$ or $f(x)$ (M1)

eg $\,\,\,\,\,$ ${7^2} + 1,{\text{ }}5 \times 7$

$g(7) = 50$ (A1)

$f\left( {50} \right) = 250$ A1 N2

METHOD 2

attempt to form composite function (in any order) (M1)

eg $\,\,\,\,\,$ $5({x^2} + 1),{\text{ }}{(5x)^2} + 1$

correct substitution (A1)

eg $\,\,\,\,\,$ $5 \times ({7^2} + 1)$

$(f \circ g)(7) = 250$ A1 N2

[3 marks]

Examiners report

[N/A]

Syllabus sections

Topic 2 - Functions and equations » 2.1 » Composite functions.

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