2.8A Function Operations

Arithmetic operations on functions

1. 2.8A Function Operations
Chapter 2 Graphs and Functions

2. Concepts and Objectives
Function operations
Arithmetic operations on functions

3. Operations on Functions
Given two functions fand g, then for all values of xfor
which both fxand gxare defined, we can also define
the following:
Sum
Difference
Product
Quotient fgxfxgx  fgxfxgx fgxfxgx 


, 0
fxf
xgx
ggx





4. Operations on Functions (cont.)
Example: Let and . Find each
of the following:
a)
b)
c)
d)
2
1fxx 35gxx  1fg  3fg 5fg 0
f
g




5. Operations on Functions (cont.)
Example: Let and . Find each
of the following:
a)
b)
c)
d)
2
1fxx 35gxx  1fg 1 1gf 
2
51 113  02 18  3fg 5fg 0
f
g




6. Operations on Functions (cont.)
Example: Let and . Find each
of the following:
a)
b)
c)
d)
2
1fxx 35gxx  1fg 1 1gf 
2
51 113  02 18  3fg  
2
353 31

 410 14 5fg 0
f
g




7. Operations on Functions (cont.)
Example: Let and . Find each
of the following:
a)
b)
c)
d)
2
1fxx 35gxx  1fg 1 1gf 
2
51 113  02 18  3fg  
2
353 31

 410 14 5fg  
2
35551

 02026 52 0
f
g




8. Operations on Functions (cont.)
Example: Let and . Find each
of the following:
a)
b)
c)
d)
2
1fxx 35gxx  1fg 1 1gf 
2
51 113  02 18  3fg  
2
353 31

 410 14 5fg  
2
35551

 02026 52 0
f
g


 
2
5
01
30


 5
1


9. Operations on Functions (cont.)
Example: Let and . Find
each of the following:
a)
b)
c)
d) 89fxx 21gxx  fgx  fgx fgx 
f
x
g




10. Operations on Functions (cont.)
Example: Let and . Find
each of the following:
a)
b)
c)
d) 89fxx 21gxx  fgx 8921xx  fgx fgx 
f
x
g




11. Operations on Functions (cont.)
Example: Let and . Find
each of the following:
a)
b)
c)
d) 89fxx 21gxx  fgx 8921xx  fgx 8921xx fgx 
f
x
g




12. Operations on Functions (cont.)
Example: Let and . Find
each of the following:
a)
b)
c)
d) 89fxx 21gxx  fgx 8921xx  fgx 8921xx fgx  8921xx 
f
x
g




13. Operations on Functions (cont.)
Example: Let and . Find
each of the following:
a)
b)
c)
d) 89fxx 21gxx  fgx 8921xx  fgx 8921xx fgx  8921xx 
f
x
g


 89
21
x
x




14. Operations on Functions (cont.)
Example: Let and . Find
each of the following:
e) What restrictions are on the domain?89fxx 21gxx

15. Operations on Functions (cont.)
Example: Let and . Find
each of the following:
e) What restrictions are on the domain?
There are two cases that need restrictions: taking the
square root of a negative number and dividing by zero. 89fxx 21gxx

16. Operations on Functions (cont.)
Example: Let and . Find
each of the following:
e) What restrictions are on the domain?
There are two cases that need restrictions: taking the
square root of a negative number and dividing by zero.
We address these by making sure the inside of gx> 0:89fxx 21gxx 210
21
1
2
x
x
x



So the domain must be 11
or ,
22
x





17. Classwork
2.8 Assignment (College Algebra)
2.8 –pg. 282: 2-14 (even); 2.7 –pg. 271: 24-36
(even); 2.6 –pg. 257: 48-52, 56 (even)
Classwork Check 2.8
Quiz 2.7