Cambridge Additional Mathematics

460 Answers

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4a b

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EXERCISE 2G

1a Domain off(x)is

fx:¡ 26 x 60 g

Range off(x)is

fy:0 6 y 65 g

Domain of f¡^1 (x)is

fx:0 6 x 65 g

Range off¡^1 (x) is

fy:¡ 26 y 60 g

b Domain off(x)is

fx:x 60 g

Range off(x)is

fy:y> 4 g

Domain of f¡^1 (x)is

fx:x> 4 g

Range off¡^1 (x) is

fy:y 60 g

c The function does not have an inverse, as it is not one-one.

d Domain off(x)is

fx:x 2 Rg

Range off(x)is

fy:y 2 Rg

Domain of f¡^1 (x)is

fx:x 2 Rg

Range off¡^1 (x) is

fy:y 2 Rg

eThe function does not have an inverse, as it is not one-one.

f Domain off(x)is

fx:x 2 Rg

Range off(x)is

fy:y> 0 g

Domain of f¡^1 (x)is

fx:x> 0 g

Range off¡^1 (x) is

fy:y 2 Rg

g Domain off(x)is

fx:x> 0 g

Range off(x)is

fy:y 63 g

Domain of f¡^1 (x)is

fx:x 63 g

Range off¡^1 (x) is

fy:y> 0 g

h The function does not have an inverse, as it is not one-one.

i Domain off(x)is

fx:x 2 Rg

Range off(x)is

fy:y 2 Rg

Domain of f¡^1 (x)is

fx:x 2 Rg

Range off¡^1 (x) is

fy:y 2 Rg

2 functioni3Range=fy:¡ 26 y< 3 g

4a i

iif¡^1 (x)=

x¡ 1

3

bi

ii f¡^1 (x)=4x¡ 2

5a if¡^1 (x)=

x¡ 5

2

ii

bif¡^1 (x)=x¡ 3

ii

cif¡^1 (x)=2x¡ 6

ii

6 f(x)is the same as

(f¡^1 )¡^1 (x)

7

02

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y

x

y=x¡¡

f(x)

f-1(x)

-2

-2

5

5

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f(x)

f-1(x)

y

4 x

4

y=x¡¡

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y

x

-3

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1

1

f-1(x)

f(x)

y=x¡¡

OO

y

x

f(x)^1

f (x)-1

1

y=x¡¡

O

y

x

y=x¡¡ f(x) = f-1(x)

2

2

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y

x

y=x¡¡ f(x)

3

3

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f-1(x)

y

x

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5

f(x)

f-1(x)

y=x

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3

y

x

f(x)

f-1(x)

y=x¡¡

3

-3

-3

O

y

3 x

f(x)^3

f-1(x)

y=x

-6

-6

O

y

x

1

1

• Qe


• Qe

y=x¡¡

f-1(x)

f(x)

O

y=x¡¡

y

x

-2

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Qw

f(x)

f-1(x)

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f-1(x)

y=x¡¡

y

x

f(x)

O

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