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)

= 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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