Compositions of Functions

Today we learned about composition of functions.

Another way of combining two functions is to form the composition of one with the other. For example, if f(x) = x^2 and g(x) = x + 1, the composition of f with g is:

f ( g( x ) )  =  f ( x + 1 )  =  ( x + 1 )^2



The composition of the function f with g is:

( f o g ) ( x )  =  f ( g ( x ) )

The domain of f o g is the set of all x in the domain of g such that g(x) is in the domain of f.


EXAMPLE:

f(x) = 2x+4      and       g(x) = x^2 - 7

(f o g) (x) = f (g(x))
                = 2(x^2 - 7) + 4

                = 2x^2 - 14 + 4
                = 2x^2 - 10