Cambridge Additional Mathematics

472 Answers

ciDomain is

fx:x> 2 g,

Range is

fy:y 2 Rg

iii

iiVA i s x=2,

x-intercept 27 ,

noy-intercept

iv x=7

v f¡^1 (x)=52+x+2

diDomain is

fx:x> 2 g,

Range is

fy:y 2 Rg

iii

iiVA i s x=2,

x-intercept 7 ,

noy-intercept

iv x=27

v f¡^1 (x)=5^1 ¡x+2

eiDomain is

fx:x> 0 g,

Range is

fy:y 2 Rg

iii

iiVA i s x=0,

x-intercept

p

2 ,

noy-intercept

iv x=2

v f¡^1 (x)=2

1 ¡ 2 x

2a i f¡^1 (x)

=ln(x¡5)

ii

iii Domain offis

fx:x 2 Rg,

Range is fy:y> 5 g

Domain off¡^1 is

fx:x> 5 g,

Range is fy:y 2 Rg

iv fhas a HAy=5,

fhasy-int 6

f¡^1 has a VAx=5,f¡^1 hasx-int 6

bif¡^1 (x)

=ln(x+3)¡ 1

ii

iii Domain offis

fx:x 2 Rg,

Range is

fy:y>¡ 3 g

Domain off¡^1 is

fx:x>¡ 3 g,

Range is

fy:y 2 Rg

iv fhas a HAy=¡ 3 ,x-intln 3¡ 1 , y-inte¡ 3

f¡^1 has a VAx=¡ 3 ,x-inte¡ 3 ,y-int ln 3¡ 1

cif¡^1 (x)

=ex+4

ii

iii Domain offis

fx:x> 0 g,

Range offis

fy:y 2 Rg

Domain off¡^1 is

fx:x 2 Rg,

Range is

fy:y> 0 g

iv fhas a VAx=0,x-int e^4

f¡^1 has a HAy=0,y-inte^4

dif¡^1 (x)

=1+ex¡^2

ii

iii Domain offis

fx:x> 1 g,

Range is

fy:y 2 Rg

Domain off¡^1 is

fx:x 2 Rg,

Range is fy:y> 1 g

iv fhas a VAx=1,

x-int1+e¡^2

f¡^1 has a HAy=1,

y-int 1+e¡^2

3aAisy=lnx

as itsx-intercept

is 1

b

c y=lnxhas

VA x=0

y=ln(x¡2)

has VAx=2

y=ln(x+2)

has VAx=¡ 2

4 y=ln(x^2 )=2lnx, so she is correct.

This is because they-values are twice as large for y=ln(x^2 )

as they are fory=lnx.

5af¡^1 :x 7 !ln(x¡2)¡ 3

bix<¡ 5 : 30 iix<¡ 7 : 61 iii x<¡ 9 : 91

iv x<¡ 12 : 2 Conjecture HA isy=2

c asx!1, f(x)!1,

asx!¡1,ex+3! 0 andf(x)! 2

) HA is y=2

d VA o ff¡^1 isx=2, Domain off¡^1 is fx:x> 2 g

6a if(5) = 3 iif(x^2 ) = log 2 (x^2 +3)

iii f(2x¡1) = 1 + log 2 (x+1)

b Domain off(x)is fx:x>¡ 3 g c x=§ 5

7aRange is fy:y> 1 g b f¡^1 (x)=^13 ln(x¡1)

c f¡^1 (10) =^13 ln 9

d Domain off¡^1 (x) isfx:x> 1 g

e (f±f¡^1 )(x)=(f¡^1 ±f)(x)=x

8af¡^1 (x)=^12 lnx

i (f¡^1 ±g)(x)=^12 ln(2x¡1)

ii(g±f)¡^1 (x)=^12 ln

³x+1

2

́

b x=13

9af(1) =^10

e

,g(6) = ln 3 b x-intercept ofg(x)is 4

c fg(x)=

10

x¡ 3

d x=ln2

10 a Domain off(x)is fx:x>¡ 6 g

b f¡^1 (x)=ex¡ 6

c x-intercept is¡ 5 ,y-intercept isln 6 dx=¡^83 or 3

REVIEW SET 5A

1a 3 b 8 c ¡ 2 d^12 e 0

f^14 g¡ 1 h^12 ,k> 0

y

x

y=x

6

O 6

f(x) = e + 5x

f-1

x=5

y=5

y

x

y=x

O

x=-3

f(x) = ex+1- 3

f-1

y=-3

y

x

x=1

y=1

y=x

OO

f-1

f(x) =ln(x - 1) + 2

7

y

x

~`2

O

y=1-2log 2 x

x=2

77

y

O x

y = 1 -log 5 (x - 2)

x=2

y

O x

y=log 5 (x-2)-2

27

y

x

y=x¡¡

OO

e 4

e 4

f-1

f(x)= x-4ln_

y

x

-2-2 11

O

y=lnx

y =ln(x + 2)

y =ln(x - 2)

-1-1 22 33

cyan magenta yellow black

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100 100 IB HL OPT
Sets Relations Groups
Y:\HAESE\CAM4037\CamAdd_AN\472CamAdd_AN.cdr Tuesday, 8 April 2014 8:33:00 AM BRIAN