Arithmetic Operations on Functions

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.

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

Videos

Functions: Adding and Subtracting

Functions: Multiplying and Dividing

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