 ## Tutoring on Determining Composite Functions and Composite Function Values

Learning Objectives:

#### Understand to Determine Composite Functions and Composite Function Values.

Math Tutoring on Determining Composite Functions and Composite Function Values

A Composite Function can be thought of as a combination of two functions. The formal definition of a composite function states, given two functions f and g, the composite function denoted using this notation f o g
f composed with g " or just " f of g"

f o g = ( f o g ) ( x ) =  f ( g ( x ) ) .

If ( f o g  ) ( x ) =  ( g o f ) ( x ) =  x , then the two functions have a special relationship. They are Inverses of one another.

The Domain of f ( g (x ) ) must contain the restrictions of the domain of g ( x ) and the composite functions.

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Hook Questions:

1.    What is a composite function?

2.    When did two functions call inverse of one another?

3.    What is the domain of f ( g (x) ) ?

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