L4 Addition and Subtraction of Functions.pdf

General Math

1. OPERATIONS OF FUNCTIONS
Addition of Functions
Subtraction of Functions
Multiplication of Functions
Division of Functions

2. OPERATIONS OF FUNCTIONS
Recall:
Rules of the operations of integers
Operations of fractions
Operations of polynomial
expressions
Factoring polynomials

3. Addition and Subtraction of Functions
Definition:
Let �and�be functions.
a)Their sum, denoted by �+�,is the function defined by
�+�??????=�??????+�??????.
b)Their difference, denoted by �−�,is the function
defined by �−�??????=�??????−�??????.

4. Addition and Subtraction of Functions
Example 1: Find the sum and difference of
1
??????−3
and
2
??????−5
.
Solutions:
1
??????−3
+
2
??????−5
=
1??????−5+2(??????−3)
(??????−3)(??????−5)
=
??????−5+(2??????−6)
??????
2
−5??????−3??????+15
=
�??????−��
??????
�
−�??????+��
1
??????−3
−
2
??????−5
=
1??????−5−2(??????−3)
(??????−3)(??????−5)
=
??????−5−2??????+6
??????
2
−5??????−3??????+15
=
−??????+�
??????
�
−�??????+��

5. Addition and Subtraction of Functions
Given: �??????=5??????−3
�??????=??????+4
Find: a. �+�??????
b. (�−�)(??????)
Solution a:
�+�??????=�??????+�??????
=5??????−3+??????+4
(�+�)(??????)=�??????+�
Solution b:
�−�??????=�??????−�??????
=5??????−3−??????+4
=5??????−3−??????−4
�−�??????=�??????−�

6. Addition and Subtraction of Functions
Given: �??????=2??????
2
−7??????−5
�??????=2??????+1
Find: a. �+�??????
b. (�−�)(??????)
Solution a:
�+�??????=�??????+�??????
=2??????
2
−7??????−5+2??????+1
=�??????
�
−�??????−�
Solution b:
�−�??????=�??????−�??????
=2??????
2
−7??????−5−2??????+1
=2??????
2
−7??????−5−2??????−1
=�??????
�
−�??????−�

7. Addition and Subtraction of Functions
Given: �??????=4??????+2??????
2
−2
�??????=4−3??????
Find: a. �+�??????
b. (�−�)(??????)
Solution a (vertical method):
�+�??????=�??????+�??????
2??????
2
+4??????−2
+ −3??????+4
�??????
�
+??????+�
Solution b(vertical method):
�−�??????=�??????−�??????
2??????
2
+4??????−2
− −3??????+4
�??????
�
+�??????−�

8. Addition and Subtraction of Functions
Function �,�and�are given by �??????=�??????
�
−��??????−�;�??????=�??????+�;and�??????=�??????−�.
Find the following:
a.) �+ℎ?????? b.) �−�?????? c.) (�+�+ℎ)(??????)
Solution b.
�−�??????=�??????−�??????
=3??????
2
−11??????−4−(3??????+1)
=3??????
2
−11??????−4−3??????−1
=�??????
�
−��??????−�
Solution a.
�+ℎ??????=�??????+ℎ??????
=3??????+1+2??????−3
=3??????+1+2??????−3
=�??????−�

9. Addition and Subtraction of Functions
Function �,�and�are given by �??????=3??????
2
−11??????−4;�??????=3??????+1;andℎ??????2??????−3.Find
the following:
a.) �+ℎ?????? b.) �−�?????? c.) (�+�+ℎ)(??????)
Solution c.
�−�??????=�??????+�??????+ℎ(??????)
=3??????
2
−11??????−4+3??????+1+2??????−3
=3??????
2
−11??????−4+3??????+1+2??????−3
=�??????
�
−�??????−�

10. Addition and Subtraction of Functions
Let �??????????????????�be two functions defined as �??????=??????
�
+�??????+�and �??????=??????+�.Find the
following:
a.) �+�2 b.) �−�1
Solution a.
�+�2=�2+�2
=??????
2
+3??????+2+??????+2
=2
2
+32+2+2+2
=12+4
=��
Solution b.
�−�1=�1−�1
=??????
2
+3??????+2−??????+2
=1
2
+31+2+1+2
=6−3
=�