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Arithmetic Operations on Functions

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In this lesson, we will look at how functions can be added, subtracted, multiplied or divided. You may also want to look at the lesson on composite functions.

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.

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:

Divide Functions 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) =
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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