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More Lessons for Algebra, Math Worksheets

In this lesson, we will look at the composition of functions or composite functions.

**What is a Composite Function?**

A composite function is a function that depends on another function. A composite function is created when one function is substituted into another function.

For example, f(g(x)) is the composite function that is formed when g(x) is substituted for x in f(x).

f(g(x)) is read as “f of g of*x*”.

f(g(x)) can also be written as (f ο g)(*x*) or fg(*x*),

In the composition (f ο g)(*x*), the domain of f becomes g(*x*).

### Videos

Composite Functions

This lesson explains the concept of composite functions. An example is given demonstrating how to work algebraically with composite functions and another example involves an application that uses the composition of functions.
Composition of Functions

Composite functions

Finding a composition of two functions

You can use the free Mathway widget below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

More Lessons for Algebra, Math Worksheets

In this lesson, we will look at the composition of functions or composite functions.

A composite function is a function that depends on another function. A composite function is created when one function is substituted into another function.

For example, f(g(x)) is the composite function that is formed when g(x) is substituted for x in f(x).

f(g(x)) is read as “f of g of

f(g(x)) can also be written as (f ο g)(

In the composition (f ο g)(

**Example:**

Given f(*x*) = 3*x* + 2 and g(*x*) = *x* + 5, find

a) (f ο g)(*x*)

b) (g ο f)(*x*)

**Solution:**

a) (f ο g)(*x*)

= f(*x* + 5)

= 3(*x* + 5) + 2

= 3*x* + 15 + 2

= 3*x* + 17

b) (g o f)(*x*)

= g(3*x* + 2)

= 3*x* + 2 + 5

= 3*x* + 7

**Example:**

Given f(*x*) = *x*^{2} + 6 and g(*x*) = 2*x* – 1, find

a) (f ο g)(*x*)

b) (g ο f)(*x*)

**Solution:**

a) (f ο g)(*x*)

= f(2*x* – 1)

= (2*x* – 1)^{2} + 6

= 4*x*^{2} – 4*x* + 2 + 6

= 4*x*^{2} – 4*x* + 8

b) (g ο f)(*x*)

= g(*x*^{2} + 6)

= 2(*x*^{2} + 6) – 1

= 2*x*^{2} + 12 – 1

= 2*x*^{2} + 11

This lesson explains the concept of composite functions. An example is given demonstrating how to work algebraically with composite functions and another example involves an application that uses the composition of functions.

Finding a composition of two functions

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

You can use the free Mathway widget below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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