Arithmetic Operations On Functions (video lessons, examples, solutions)

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
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Algebraic Expressions
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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)
= 5×2 + 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) = 3×2 + 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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