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Composite Functions




 
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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).

Example:

Given f(x) = 3x + 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
= 3x + 15 + 2
= 3x + 17

b) (g o f)(x)
= g(3x + 2)
= 3x + 2 + 5
= 3x + 7

Example:

Given f(x) = x2 + 6 and g(x) = 2x – 1, find

a) (f ο g)(x)
b) (g ο f)(x)

Solution:

a) (f ο g)(x)
= f(2x – 1)
= (2x – 1)2 + 6
= 4x2 – 4x + 2 + 6
= 4x2 – 4x + 8

b) (g ο f)(x)
= g(x2 + 6)
= 2(x2 + 6) – 1
= 2x2 + 12 – 1
= 2x2 + 11




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

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