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6.1 Composite Functions

Dive into evaluating composite functions, finding their domains and ranges, and understanding function compositions. Discover how order matters in composing functions and find solutions for decomposing functions into simpler components.

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6.1 Composite Functions

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  1. 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 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. 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

  4. Use the function CLOSEST to the input value FIRST Compositions of Functions 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. Example Express as a composition of two functions f and gsuch that . 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.

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

  9. End of Section 6.1

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