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Date	May 2014	Marks available	2	Reference code	14M.1.sl.TZ2.3
Level	SL only	Paper	1	Time zone	TZ2
Command term	Find	Question number	3	Adapted from	N/A

Question

The following diagram shows the graph of $y = f(x)$ , for $- 4 \le x \le 5$ .

Write down the value of $f( - 3)$ .

[1]

a(i).

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

[1]

a(ii).

Find the domain of ${f^{ - 1}}$ .

[2]

b.

On the grid above, sketch the graph of ${f^{ - 1}}$ .

[3]

c.

Markscheme

$f( - 3) = - 1$ A1 N1

[1 mark]

a(i).

${f^{ - 1}}(1) = 0$ (accept $y = 0$ ) A1 N1

[1 mark]

a(ii).

domain of ${f^{ - 1}}$ is range of \(f\) (R1)

eg ${\text{R}}f = {\text{D}}{f^{ - 1}}$

correct answer A1 N2

eg $- 3 \leqslant x \leqslant 3,{\text{ }}x \in [ - 3,{\text{ }}3]{\text{ (accept }} - 3 < x < 3,{\text{ }} - 3 \leqslant y \leqslant 3)$

[2 marks]

b.

A1A1 N2

Note: Graph must be approximately correct reflection in $y = x$ .

Only if the shape is approximately correct, award the following:

A1 for x-intercept at $1$ , and A1 for endpoints within circles.

[2 marks]

c.

Examiners report

[N/A]

a(i).

[N/A]

a(ii).

[N/A]

b.

[N/A]

c.

Syllabus sections

Topic 2 - Functions and equations » 2.1 » Concept of function

$f:x \mapsto f\left( x \right)$ .

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