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)

= 5x^{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:**

- f(x) = x
^{2}+ 3x

g(x) = 8x + 9

(f+g)(x) = f(x) + g(x) = ? - f(x) = x
^{2}+ 2x + 8

g(x) = 3x^{2}- x + 7

(f-g)(x) = f(x) - g(x) = ?

**Functions: Multiplying And Dividing**

**Example:**

f(x) = (x^{2} - 1)

g(x) = (x + 1)

(fg)(x) = ?

(f/g)(x) = ?

**Combining Functions By Addition Subtraction Multiplication And Division**

**Example:**

f(x) = 3x^{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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