Pronunciation: /kəmˈpɒz.ɪt ˈfʌŋk.ʃən/ Explain
|Figure 1: Composite function||
A composite function is a
that is made up of two other functions that takes as input of one function the output of
the other function. To write the composition
of functions f(x) and g(x), write
f(x) ° g(x) or f(g(x)).
A composite function is sometimes called a compound function.
The act of composing functions is called composition of functions.
Properties of composite functions
Some properties of composite functions are:
||f ° (g ° h(x))
= (f ° g) ° h(x)
||Composition of functions is associative.|
||f ° g(x) ≠ g ° f(x)
||Composition of functions is not commutative.|
||f ° f-1(x) = x
||The composition of a function and its inverse is the identity function
(f(x) = x).|
||f(x) = ax + b, g(x)
= cx + d, f(g(x)) = acx + ad+b
||The composition of two linear functions is also linear.|
|Polynomials||The degree of the composition of two polynomials is the product of the degrees of the two functions.|
|Table 1: Properties of composite functions|
Check one check box on the left and one on the right to see the two functions and their composite.|
Does f(g(x)) always equal g(f(x))?
|Manipulative 1 - Composite Functions Created with GeoGebra.|
- McAdams, David E.. All Math Words Dictionary, composite function. 2nd Classroom edition 20150108-4799968. pg 40. Life is a Story Problem LLC. January 8, 2015. Buy the book
- composite function. merriam-webster.com. Encyclopedia Britannica. Merriam-Webster. Last Accessed 6/25/2018. http://www.merriam-webster.com/dictionary/composite function. Buy the book
- Goldrei, D.C.. Classic Set Theory: For Guided Independent Study. pg 5. Chapman & Hall Mathematics. July 1 1996. Last Accessed 6/25/2018. Buy the book
- R. K. Singh, J. S. Manhas. Composition Operators on Function Spaces. North-Holland. November 1 1993. Last Accessed 6/25/2018. Buy the book
- Carl C. Cowen, Barbara I. Maccluer. Composition Operators on Space of Analytic Functions. CRC-Press. June 30 1995. Last Accessed 6/25/2018. Buy the book
- McAdams, David E.. Composite. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 6/27/2018. http://www.allmathwords.org/en/c/composite.html.
Cite this article as:
McAdams, David E. Composite Function. 4/14/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/c/compositefunction.html.
4/14/2019: Updated equations and expressions to new format. (McAdams, David E.)
12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)
6/25/2018: Removed broken links, updated license, implemented new markup, updated GeoGebra apps. (McAdams, David E.)
5/5/2011: Initial version. (McAdams, David E.)