OPERATIONS OF FUNCTIONhshdhsbdbbsbvvj.pdf

It is helpful to the student who wants to learn about mathematics.

1. OPERATIONS
OFFUNCTION
MYLAM.ARONDA

2. OBJECTIVES
A.defineoperationoffunctions.
B.substituteeachvalueinagiven
equation
C.Performtheindicatedoperation

3. DEFINITION
Letfandgbefunctionsdefinedatarealnumberx.
thesum,difference,product,andquotientfunctionsf
andgarethefunctionsdefinedby
(f+g)(x)=f(x)+g(x) sumfunction
(f-g)(x)=f(x)–g(x) differencefunction
(fg)(x)=f(x)g(x) productfunction
,g(x)≠0 quotientfunction

4. EXAMPLE
IN
SUMFUNCTION

5. EXAMPLE
Giventhefunctions:
�(??????)=??????+5
�(??????)=2??????−1
ℎ(??????)=2+9??????−5
Find:(f+g)(x)
(g+h)(x)

6. Find(f+g)(x)
Given:�(??????)=??????+5
�(??????)=2??????−1
Solution:
(f+g)(x)=f(x)+g(x)
(f+g)(x)=(x+5)+(2x-1)
=x+2x+5–1
=3x+4
Definitionofaddition
replacef(x)andg(x)bythe
givenvalues.Combinelike
termsandperformthe
indicatedvalues

7. Find(g+h)(x)
Given:�(??????)=2??????−1
ℎ(??????)=2+9??????−5
Solution:
(g+h)(x)=g(x)+h(x)
=(2x-1)+(2+9??????−5
=2+2x+9x–5-1
=2+11x-6
Definitionofaddition
replacef(x)andg(x)bythe
givenvalues.Combinelike
termsandperformthe
indicatedvalues

8. EXAMPLE
IN
DIFFERENCE
FUNCTION

9. EXAMPLE
Giventhefunctions:
�(??????)=??????+5
�(??????)=2??????−1
ℎ(??????)=2+9??????−5
Find:(f-g)(x)
(g-h)(x)

10. Find:(f-g)(x)
Given:�(??????)=??????+5
�(??????)=2??????−1
Solution:
(f–g)(x)=f(x)–g(x)
=(x+5)–(2x-1)
=x+5-2x+1
=x-2x+5+1
=-x+6
Definitionofsubtractionof
functionsreplacef(x)andg(x)by
thegivenvaluesandgivenvalues
anddistributethenegativesign.
combineliketermsandperformthe
indicatedoperation

11. Find(g-h)(x)
Given:�(??????)=2??????−1
ℎ(??????)=2+9??????−5
Solution
(g–h)(x)=g(x)–h(x)
=(2x–1)–(2+9??????−5)
=2x-1-29??????+5
=-2-9x+2x+5-1
=-2-7x+4
Definitionofsubtractionof
functionsreplacef(x)andg(x)by
thegivenvaluesandgivenvalues
anddistributethenegativesign.
combineliketermsandperformthe
indicatedoperation

12. EXAMPLE
IN
PRODUCT
FUNCTION

13. EXAMPLE
Giventhefunctions:
f(x)=2x-1 g(x)=+1 h(x)=3x-
4
Find:(gh)(x)
(fh)(x)

14. Find:(gh)(x)
Given:g(x)=+1
h(x)=3x-4
Solution
(gh)(x)=g(x)•h(x)
=+1)(3x-4)
=+3x-4-4
=-4+3x-4
Definitionofmultiplicationof
functions.Replacef(x0andg(x)
bythegivenvalues.Multiplythe
binomial

15. Find:(fh)(x)
Given:f(x)=2x-1
h(x)=3x-4
Solution:
(fh)(x)=f(x)•h(x)
=(2x-1)(3x-4)
=6-3x–8x+4
=6-11x+4
Definitionofmultiplicationof
functions.Replacef(x0and
g(x)bythegivenvalues.
Multiplythebinomial

16. EXAMPLE
IN
QUOTIENT
FUNCTION

17. EXAMPLE
Giventhefunctions:
�(??????)=??????+5
�(??????)=2??????−1
ℎ(??????)=2+9??????−5
Find:
(x)

18. Find:(x)
GIVEN:�(??????)=2??????−1
ℎ(??????)=2+9??????−5
Solution:
(x)=
=
=
=x+5
Definitionofdivisionoffunctions
replaceh(x)andg(x)bythegiven
valuesfactorthenumerator
canceloutthecommonfactors.

19. Find:(x)
Given:ℎ(??????)=2+9??????−5
�(??????)=??????+5
Solution:
(x)=
=
=
=2x-1
Definitionofdivisionoffunctions
replaceh(x)andg(x)bythegiven
valuesfactorthenumerator
canceloutthecommonfactors.