Math

Composition of Functions

In mathematics, a Function Composition represented by a circle is an operation that combine two functions f(x) and g(x) to produce a function h(x):

                                                       

In a composition of functions, the domain of the first function f(x) becomes g(x). Therefore, in order to find the final function h(x), one has to replace x in f(x) by g(x).

Example: For  and , find 

In order to solve this problem, we have to replace x in f(x) by g(x):

Example: Find the composite function for and 

Example: Find the domain of the composite functions 

a) First, we need to find the composite function by replacing x by f(x):

, the domain of the function is all real numbers.

b) We find the composite function:

the domain is