# Arithmetic Operations On Functions

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

The following diagram shows the operations with functions: addition, subtraction, multiplication, and division. Scroll down the page for more examples and solutions on function operations. 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) = ?

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations. 