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.
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:
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 out our new and fun Fraction Concoction Game.
Add and subtract fractions to make exciting fraction concoctions following a recipe. There are four levels of difficulty: Easy, medium, hard and insane. Practice the basics of fraction addition and subtraction or challenge yourself with the insane level.
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