# Arithmetic Operations on Functions

Related Topics:
More Lessons for Algebra, Math Worksheets

In this lesson, we will look at how functions can be added, subtracted, multiplied or divided. You may also want to look at the lesson on composite functions.

Example

Add the functions f(x) = x + 2 and g(x) = 5x – 6

Solution:

(f + g)(x)
= f(x) + g(x)
= (x + 2) + (5x – 6)
= 6x – 4

Functions can be subtracted

Example:

Given f(x) = x + 2 and g(x) = 5x – 6, find (f – g)(x)

Solution:

(f – g)(x)
= f(x) – g(x)
= (x + 2) – (5x – 6)
= –4x + 8

Functions can be multiplied.

Example:

Add the functions f(x) = x + 2 and g(x) = 5x – 6

Solution:

(f • g)(x)
= f(x) • g(x)
= (x + 2)(5x – 6)
= 5x2 + 4x – 12

Functions can be divided.

Example:

Given f(x) = x + 2 and g(x) = 5x – 6, find

Solution:

for g(x) ≠ 0

Examples:
1. f(x) = x2 + 3x
g(x) = 8x + 9
(f+g)(x) = f(x) + g(x) =

2. f(x) = x2 + 2x + 8
g(x) = 3x2 - x + 7
(f-g)(x) = f(x) - g(x) =
Functions: Multiplying and Dividing
Example:
f(x) = (x2 - 1)
g(x) = (x + 1)
(fg)(x) =
(f/g)(x) =
Combining Functions by Addition Subtraction Multiplication and Division
Example:
f(x) = 3x2 + 4
g(x) = x - 5
(f + g)(x) =
(f - g)(x) =
(fg)(x) =
(f/g)(x) =
Sum, Difference, Product and Quotient of Two Functions
How to find the sum, difference, product and quotient of two functions and determine the domain?
Example:
f(x) = 5x - 4
g(x) = -9x + 6
(f + g)(x) =
(f - g)(x) =
(fg)(x) =
(f/g)(x) =

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