Decomposition of Composite Functions

Opening Prayer

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​Objectives:

• I can ​recognize notation for function composition.

• I can ​form a composite function using two given functions.

• I can evaluate ​a composite function.

• ​I can give situations where composite functions can be applied.

​F(x)

​G(x)

​F[G(x)]

​G[F(x)]

​The function as a machine...

Definition

​​The process of obtaining a composite function is called function composition.

Example:

You may need to evaluate a composite function for a particular value of x.

1. Find and simplify (g o f)(x).

2. Find and simplify (q o f)(x). Is it the same with (q o f)(x)? 3. Find and simplify (f o r)(x).

4. Find and simplify (F o r)(5).

Essential Questions:

1. How do you define composite functions?

2. ​How are they different from functions?