If  f : A→ B  and  g : A→ B  exist, then there is a function  mapping  h : A→ C .

Function h is the composition of functions f  and g and  h(x) = f (g (x)).

 

Example

 

If  f ( x)  = 2x  1  and g ( x)  = 3x² + 2x  1  find

 

a)    f (g (x))

b)   g (f (x))

 

 

a)    f (g (x)) = f (3x² + 2x  1 )

                  = 2(3x² + 2x  1 ) -1

                  = 6x² + 4x  3

 

 

b)   g (f (x)) = g (2x  1)

                  = 3(2x  1)² + 2(2x  1)  1

                  = 3(4x² - 4x + 1) + 4x  3

                  = 12x² - 12x +3 + 4x  3

                  = 12x²  8x