Now we need to discuss the new method of combining functions. The new way of combining functions is called function composition. Following is the definition.

Given two functions

f ( x ) and g ( x )we have the given two definitions.

1.      The composition of  f ( x ) & g ( x ) (note the order here) is,

                              ( f o g ) ( x ) = f [g ( x )]

2.   The composition of g ( x ) & f ( x ) (again, note the order) is,

                                                  ( g o f ) ( x ) =g [f ( x )]