Related Topics:

More Lessons for Algebra

Math Worksheets

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: Adding and Subtracting**

Examples:

1. f(x) = x^{2} + 3x

g(x) = 8x + 9

(f+g)(x) = f(x) + g(x) =

2. 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) =

More Lessons for Algebra

Math Worksheets

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.

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

Examples:

1. f(x) = x

g(x) = 8x + 9

(f+g)(x) = f(x) + g(x) =

2. f(x) = x

g(x) = 3x

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

Example:

f(x) = (x

g(x) = (x + 1)

(fg)(x) =

(f/g)(x) =

Example:

f(x) = 3x

g(x) = x - 5

(f + g)(x) =

(f - g)(x) =

(fg)(x) =

(f/g)(x) =

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) =

Try the free Mathway calculator and
problem solver below to practice various math topics. Try the given examples, or type in your own
problem and check your answer with the step-by-step explanations.

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.