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Date May 2022 Marks available 2 Reference code 22M.1.AHL.TZ2.10
Level Additional Higher Level Paper Paper 1 Time zone Time zone 2
Command term Solve Question number 10 Adapted from N/A

Question

The function fx=ln1x-2 is defined for x>2, x.

Find an expression for f-1(x). You are not required to state a domain.

[3]
a.

Solve fx=f-1(x).

[2]
b.

Markscheme

y=ln1x-2

an attempt to isolate x (or y if switched)         (M1)

ey=1x-2

x-2=e-y

x=e-y+2

switching x and y (seen anywhere)          M1

f-1(x)=e-x+2          A1


[3 marks]

a.

sketch of fx and f-1(x)          (M1)

x=2.12  2.12002          A1


[2 marks]

b.

Examiners report

This question was well answered by most candidates.

a.
[N/A]
b.

Syllabus sections

Topic 2—Functions » SL 2.2—Functions, notation domain, range and inverse as reflection
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