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Date May 2015 Marks available 2 Reference code 15M.1.sl.TZ1.4
Level SL only Paper 1 Time zone TZ1
Command term Find Question number 4 Adapted from N/A

Question

The following diagram shows the graph of a function \(f\).

Find \({f^{ - 1}}( - 1)\).

[2]
a.

Find \((f \circ f)( - 1)\).

[3]
b.

On the same diagram, sketch the graph of \(y = f( - x)\).

[2]
c.

Markscheme

valid approach     (M1)

eg\(\;\;\;\)horizontal line on graph at \( - 1,{\text{ }}f(a) =  - 1,{\text{ }}( - 1,5)\)

\({f^{ - 1}}( - 1) = 5\)     A1     N2

[2 marks]

a.

attempt to find \(f( - 1)\)     (M1)

eg\(\;\;\;\)line on graph

\(f( - 1) = 2\)     (A1)

\((f \circ f)( - 1) = 1\)     A1     N3

[3 marks]

b.

     A1A1     N2

 

Note:     The shape must be an approximately correct shape (concave down and increasing). Only if the shape is approximately correct, award the following for points in circles:

A1 for the \(y\)-intercept,

A1 for any two of these points \(( - 5,{\text{ }} - 1),{\text{ }}( - 2,{\text{ }}1),{\text{ }}(1,{\text{ }}2)\).

[2 marks]

Total [7 marks]

c.

Examiners report

Typically candidates were more successful in finding the composite function than the inverse. Some students tried to find the function, rather than read values from the given graph. The sketch of \(f( - x)\) was often well done, with the most common error being a reflection in the x-axis.

a.

Typically candidates were more successful in finding the composite function than the inverse. Some students tried to find the function, rather than read values from the given graph. The sketch of \(f( - x)\) was often well done, with the most common error being a reflection in the x-axis.

b.

Typically candidates were more successful in finding the composite function than the inverse. Some students tried to find the function, rather than read values from the given graph. The sketch of \(f( - x)\) was often well done, with the most common error being a reflection in the x-axis.

c.

Syllabus sections

Topic 2 - Functions and equations » 2.1 » Identity function. Inverse function \({f^{ - 1}}\) .
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