Pronunciation: /kəmˈpɒz.ɪt ˈfʌŋk.ʃən/ Explain
|Figure 1: Composite function||
A composite function is a
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:
|Associative||f°(g°h(x)) = (f°g)°h(x)||Composition of functions is associative.|
|Commutative||f°g(x) ≠ g°f(x)||Composition of functions is not commutative.|
|Inverse functions||f°f-1(x)= x||The composition of a function and its inverse is the identity function (f(x)=x).|
|Linear functions||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. 3/9/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/c/compositefunction.html.
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.)