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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).

Write down the value of  \({f^{ - 1}}(1)\).

[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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