7.6b Compositions of Functions
If you have made mistakes, even serious ones, there is
always another chance for you. What we call failure is not
the falling down but the staying down.
Composition of Functions
The composition of function f with function g is
written f g and is defined as  f g  ( x)  f ( g ( x)).
f
g  ( x)  f ( g ( x))
“f of g of x”
1
2
1) Evaluate the inner function g(x) first.
2) Then use your result as the input of the outer function f (x).
Composition of Functions
Let f ( x)  2 x  3 and g ( x)  x 2
Ex1) Find (f g )( x)
Ex2) Find (g f )( x)
Composition of Functions
Let f ( x)  3x  1 and g ( x)  2 x 2  4 (two different ways)
Ex3) Find ( f g )(1)
Ex4) Find ( g f )( 3)
7.6b Compositions of Functions
HW 7.6b: 23-43 odd
If you have made mistakes, even serious ones, there is
always another chance for you. What we call failure is not
the falling down but the staying down.