Arithmetic Operations On Functions

When we talk about arithmetic operations on functions, we mean combining two or more functions using the basic operations of addition, subtraction, multiplication, and division to create a new function.

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

Check out our most popular games!

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