Main Concept

Sometimes it is useful to apply one function, and then apply a second function to the result. For example, suppose  and . First,   takes the input value  and outputs . Then,  is input into  which gives a new output, . This idea can be used to create a new function, called the composition of g and f.

Let  and  be two functions. The composition of the functions  and , written   ("g composed with f "), is defined by

The domain of the function   is the set of all numbers  in the domain of  for which  is in the domain of .