Cambridge Additional Mathematics

Answers 461

8 f¡^1 (x)=^1

x

andf(x)=^1

x

) f=f¡^1

) fis a self-inverse function

9af¡^1 (x)=2x+2

bi(f±f¡^1 )(x)=x ii (f¡^1 ±f)(x)=x

10 a 10

bf¡^1 (x)=

x¡ 5

2

and f¡^1 (¡3) =¡ 4

g¡^1 (x)=8¡ 2 x and g¡^1 (6) =¡ 4

) f¡^1 (¡3)¡g¡^1 (6) = 0

cx=3

11 a i 25 ii 16 bx=1

12 aIs not b Is c Is dIs eIs f Is not

13 (f¡^1 ±g¡^1 )(x)=

x+3

8

and (g±f)¡^1 (x)=

x+3

8

REVIEW SET 2A

1afunction b function c not a function dfunction

2 a=¡ 6 ,b=13

3ax=¡ 2 or 12 b x=¡ 5 or 1

4a 10 bx^2 ¡x¡ 2

5a iDomain isfx:x>¡ 3 g, Range isfy:y> 2 g

ii function is one-one

biDomain isfx:x 2 Rg, Range isfy:y>¡ 5 g

ii function is not one-one

ciDomain isfx:x 2 Rg,

Range isfy:y=¡ 3 ory=1g

ii function is not one-one

6a b

7

8a b

9a 2 x^2 +1 b 4 x^2 ¡ 12 x+11

10 a b

cThe function does not have an inverse.

11 af¡^1 (x)=x¡^2

4

bf¡^1 (x)=^3 ¡^4 x

5

12 a f(¡3) = (¡3)^2 =9

g(¡^43 )=1¡6(¡^43 )=9

b 169 c x=¡ 4

13 (f¡^1 ±h¡^1 )(x)=(h±f)¡^1 (x)=x¡ 2

REVIEW SET 2B

1anot a function b function, one-one

cfunction, not one-one

2a 12 bx=§ 1

3ax=¡ 5 or 6 b x=1or 3

4a b

5a 10 ¡ 6 x b 9 x¡ 14 c ¡ 23

6 fy:3 6 y 67 g 7

8a i 1 ¡ 10 x ii 5 ¡ 10 x bx=¡^35

9 a=1, b=¡ 6 , c=5

10 a c

bThe function does not have an inverse.

11 af¡^1 (x)=

7 ¡x

4

bf¡^1 (x)=

5 x¡ 3

2

12 (f¡^1 ±h¡^1 )(x)=(h±f)¡^1 (x)=

4 x+6

15

1316

EXERCISE 3A.1

1ax=0,¡^74 bx=0,¡^13 c x=0,^73

dx=0,^112 ex=0,^83 f x=0,^32

gx=3, 2 hx=4,¡ 2 i x=3, 7

j x=3 kx=¡ 4 , 3 l x=¡ 11 , 3

2ax=^23 bx=¡^12 , 7 c x=¡^23 , 6

dx=^13 ,¡ 2 ex=^32 , 1 f x=¡^23 ,¡ 2

gx=¡^23 , 4 hx=^12 ,¡^32 i x=¡^14 , 3

j x=¡^34 ,^53 kx=^17 ,¡ 1 l x=¡ 2 ,^2815

3ax=2, 5 bx=¡ 3 , 2 c x=0,¡^32

dx=1, 2 ex=^12 ,¡ 1 f x=3

• We 4

-+-x

-2 3

--+x

y

x

2

2

y=x¡¡

f-1(x)

f(x)

OO

y

x

2

5

25

f-1(x) y=x¡¡

f(x)

O

y

O 3 x

1

y= 1- x||Qe

1

+-x

y

x

-2

-2

2

2

f-1(x)

f(x)

y=x¡¡

O

y

x

f(x)^3

f (x)-1

3

y=x

O

-2 3

--+x

y

O x

1

Qw

y= 2x-1||

y

x

y = (x)¦

O

y = f(x)||

y

x

y = (x)¡¦

O

y = f(x)||

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