addmath form 4 Chapter 1 - Function

ADDITIONAL MATHEMATICS CHAPTER 1 : FUNCTION

BY : cg.aiman FUNCTIONS Function

Relations 1. #rro #rro$ $ %iag %iagra ram m

• • • •

ON! to ON! ON! to "#NY "#NY to ON! "#NY to "#NY

Function

f:2

Comosite

inverse function

f'2+ 3 4

fg'2+ 3 f 

4

f 51'4+ 3 2

Or  888888888888   888888888888 

1. Or%e Or%ere re% % air airs s

gf 

&'()*+)',)-+) '*)1+/

g 2

(. ras

f  4

1.0Relation f 51

g51

!2ress te relation et$een te follo$ing airs of set in te form of arro$ %iagram) or%ere% air an% gra. #rro$ %iagram a+ Set # 3 &;elantan) Selangor) / Relation: =Numer of e%ge? c+ Set # 3 & -) 1) */ Set B 3 & *) ( ,/ Relation: =S@uare root of numer?

Or%ere% air

ra

9

!2ress te relation et$een te follo$ing airs of set in te form of arro$ %iagram) or%ere% air an% gra. #rro$ %iagram

Or%ere% air

ra

a+ Set # 3 &;elantan) Selangor) / Relation: =Numer of e%ge? c+ Set # 3 & -) 1) */ Set B 3 & *) ( ,/ Relation: =S@uare root of numer? %+ Set 2 3 & () >) ) A/ Set 4 3 & *) 1() 10) 1*/ Relation: (2

1.1etermine %omain) co%omain) oect) image an% range of relation Dist %o$n te %omain) co%omain) oect) image an% range of te follo$ing realtion

omain

3 &EEEEEEEEEE/

Co%omain 3 &EEEEEEEEEE./ Oect

3 EEEEEEEEEEE

Image

3 EEEEEEEEEE..

Range

3 &EEEEEEEEEE/

State te t4e of te follo$ing relation

1.1etermine %omain) co%omain) oect) image an% range of relation

State te t4e of te follo$ing relation

Dist %o$n te %omain) co%omain) oect) image an% range of te follo$ing realtion

omain

3 &EEEEEEEEEE/

Co%omain 3 &EEEEEEEEEE./ Oect

3 EEEEEEEEEEE

Image

3 EEEEEEEEEE..

Range

3 &EEEEEEEEEE/

(.0 Function 1.(Classif4ing te t4es of te relations

a+ Fin% te image for eac of te follo$ing function i+f:2 (2  f'>+ 3

 x

ii+g:2

5

  

iii+'2+ 3 ⎸2 5 ,⎹ Gn% '*+ an%   '5,+.

!H!RCIS! 'CDON! #SS Y!#R S"+ 1. iven te function f:x  ⎸2 5 (⎹) Gn% te values of 2 suc tat f'2+ 3 . (00A aer 1:@uestion (

Gn% g'5,+

+ Fin% te oect for eac of te follo$ing function i+ f'2+ 3 (2  A for $ic f'2+ 3,

8

ii+ g'2+ 3

2  x + 1

for $ic g'2+ 3 *

iii+ '2+ 3 ⎸2 5 ,⎹ for $ic ave te image >.

(. It is given tat te function f(x)3 p J , x ) $ere  is a constant. Fin% te value of  suc tat f ' p+ 3* (01( aer 1: @uestion ,

a+ Fin% te image for eac of te follo$ing function i+f:2 (2  f'>+ 3

 x

ii+g:2

5

  

iii+'2+ 3 ⎸2 5 ,⎹ Gn% '*+ an%   '5,+.

!H!RCIS! 'CDON! #SS Y!#R S"+ 1. iven te function f:x  ⎸2 5 (⎹) Gn% te values of 2 suc tat f'2+ 3 . (00A aer 1:@uestion (

Gn% g'5,+

+ Fin% te oect for eac of te follo$ing function i+ f'2+ 3 (2  A for $ic f'2+ 3,

8

ii+ g'2+ 3

2  x + 1

iii+ '2+ 3 ⎸2 5 ,⎹ for $ic ave te image >.

for $ic g'2+ 3 *

(. It is given tat te function f(x)3 p J , x ) $ere  is a constant. Fin% te value of  suc tat f ' p+ 3* (01( aer 1: @uestion ,

,.0 Comosite function

,.1 a+ Fin% te follo$ing comosite functions. i+f'2+ 3 (2  , g'2+ 3 152 fg'2+ 3

ii+ g'2+ 3 ( >2 Gn% g('2+

,.1 c+ Solve  x

iii+ g'2+ 3 1 5

2 4

'2+ 3  

 x

g'2+3

,.1 + Fin% te value for eac of te follo$ing comosite functions. i+f'2+ 3 (2  , g'2+ 3 152   fg'*+

ii+ f'2+ 3 (2  , g'2+ 3 (  >2( gf',+ 3

iii+ f'2+ 3 (2  1 g'2+ 3 a2(   gf'2+ 3 1(2(  1(2  A a+Gn% a an%  + Gn% g('>+

,.1 a+ Fin% te follo$ing comosite functions. i+f'2+ 3 (2  , g'2+ 3 152 fg'2+ 3

ii+ g'2+ 3 ( >2 Gn% g('2+

,.1 c+ Solve  x

iii+ g'2+ 3 1 5

2 4

'2+ 3  

 x

g'2+3

,.1 + Fin% te value for eac of te follo$ing comosite functions. i+f'2+ 3 (2  , g'2+ 3 152   fg'*+

ii+ f'2+ 3 (2  , g'2+ 3 (  >2( gf',+ 3

iii+ f'2+ 3 (2  1 g'2+ 3 a2(   gf'2+ 3 1(2(  1(2  A a+Gn% a an%  + Gn% g('>+

!H!RCIS! 'CDON! #SS Y!#R S"+ *.0 Inverse function

12

1. iven te function '2+ 3

 x

)2

≠

 0 an%

te comosite function g'2+ 3 *2) Gn% a+ g'2+ + te value of 2 $en g'2+ 3 K (00* aer 1: @uestion ,

(. L : 2 2  @) $ere  an% @ are constants) an%  M 0. L( : 2 (>2  *( Fin% te values of  an% @.

f'2+ 3 4 f 51'4+ 3 2 a+ Fin% te inverse function of eac of te follo$ing functions.

!H!RCIS! 'CDON! #SS Y!#R S"+ *.0 Inverse function

12

1. iven te function '2+ 3

 x

)2

≠

 0 an%

te comosite function g'2+ 3 *2) Gn% a+ g'2+ + te value of 2 $en g'2+ 3 K (00* aer 1: @uestion ,

f'2+ 3 4 f 51'4+ 3 2 a+ Fin% te inverse function of eac of te follo$ing functions.

(. L : 2 2  @) $ere  an% @ are constants) an%  M 0. L( : 2 (>2  *( Fin% te values of  an% @. (00A: aer 1:@uestion,

+ Fin% te inverse function of eac of te follo$ing function in term of  an% @.

Solving comosite an% inverse function  x

a+ iven tat f '2+ 3 a2  an% f 51 '2+ 3

−3 4

)

Gn% i+Te values of a an%  ii+ Te value of f'5+ iii+Te value of  51',+

+ iven te functions g '2+ 3 ,2 1 an% '2+ 3 2(

+ Fin% te inverse function of eac of te follo$ing function in term of  an% @.

Solving comosite an% inverse function  x

a+ iven tat f '2+ 3 a2  an% f 51 '2+ 3

−3 4

)

Gn% i+Te values of a an%  ii+ Te value of f'5+ iii+Te value of  51',+

+ iven te functions g '2+ 3 ,2 1 an% '2+ 3 2( J 2  () Gn% i+te value of g 51'(+ ii+te comosite function g'2+.

S" #SS Year !2am 1. 'sm (01*)aer 1) 1+

S" #SS Year !2am 1. 'sm (01*)aer 1) 1+

(. 'Sm (01*) aer 1)(+

,. 'sm (01*) aer () ,+

*. 'sm (01,) aer 1) 1+

>. 'sm (01,) aer 1) (+

. 'sm (01,) aer 1) ,+

A. 'sm) (01() aer 1) 1+

K. 'sm (01() aer 1) (+

-. 'sm (01() aer 1) ,+