Arithmetic Operations On Functions

Related Pages
Adding & Subtracting Polynomials
Algebra Terms
Algebraic Expressions
More Algebra Lessons

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.

Functions Can Be Added

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

Functions: Adding And Subtracting

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) = ?

• Show Video Lesson

Functions: Multiplying And Dividing

Example:
f(x) = (x² - 1)
g(x) = (x + 1)
(fg)(x) = ?
(f/g)(x) = ?

• Show Video Lesson

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) = ?

• Show Video Lesson

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) = ?

• Show Video Lesson

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.

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.