Intermediate Algebra – Student Workbook – Second Edition 2013

Lesson 2b – Functions and Function Operations
Mini-Lesson
Function Division and the Division Property of Exponents
When dividing functions, you will also need to work with exponents of different powers. The
following should be familiar to you and will come into play in the examples below:
DIVISION PROPERTY OF EXPONENTS
Let m, n be rational numbers. To divide powers of the same base, keep the base and subtract the
exponents.
a
a
m
n
mn
a where a 0
Problem 9 WORKED EXAMPLE – FUNCTION DIVISION
For each of the following, find f (x) . Use only positive exponents in your final answer.
g(x)
a) ( ) and ( )
f ( x)
15x
g(
x)
3x
5x
5x
159
6
15
9
b) ( ) and ( )
f ( x)
4x
8
g(
x)
2x
2x
2x
5
58
3
This is not our final answer, however, as we need to use only positive exponents in our
final result. Recall the rule for negative exponents as follows: If a 0 and n is a rational
number, then
a
n
1
n
a
Let’s use this rule to rewrite as follows:
3 2
f ( x)
2
2x
Therefore, our final results are:
3
3
x
g(
x)
x
Notice that the -2 on top did not change or impact the exponent in any way.
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