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

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!

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.

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:

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

Example Solution:

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 .

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

MAT 204 F08 End of Section 6.1