1. MAT 204 F08
6.1 Composite Functions
In this section, we will study the following topics:
Evaluating composite functions
Finding domain and range of composite functions

2. Compositions of Functions
Definition of Composition of Two Functions
The domain of is the set of all x in the domain of g such that g(x) is in the domain of f.
The composition of functions means that you will first evaluate x in the function g. Then you will take that result and evaluate it in function f.
So you evaluate in one function and then the result in the other.
Just be careful; ORDER MATTERS!

3. Compositions of Functions
means evaluate x first in g, then the result in f.
means evaluate x first in f, then the result in g.

4. Compositions of Functions
Use the function CLOSEST to the input value FIRST
So if then to find
you would first evaluate g at x = –1:
Then you would evaluate f using this result:
Write out complete answer:

5. Compositions of Functions (continued)
Take a look*:
Solution:
State the domain of each composite function.

6. Example
Solution:

7. Decomposition of Functions
Sometimes we decompose functions, which, I assure you, has nothing to do with rotting flesh.
To decompose a function, we basically write a given function as a composition of two or more functions.
Example
Express as a composition of two functions f and g such that

8. Example
Express as a composition of two functions f and g such that

9. MAT 204 F08
End of Section 6.1