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.
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:
- f(x) = x2 + 3x
g(x) = 8x + 9
(f+g)(x) = f(x) + g(x) = ? - 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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