1. Composite Functions Example 1:Given functions f(x) = x 2 – 3x and g(x) = 2x + 1, find f  g. The notation "f  g" means f (g(x)). In other words, replace x in function f with 2x + 1 (the g function). f (x ) = (x) 2 – 3(x)

2. Composite Functions Example 1:Given functions f(x) = x 2 – 3x and g(x) = 2x + 1, find f  g. The notation "f  g" means f (g(x)). In other words, replace x in function f with 2x + 1 (the g function). f (x ) = ( ) 2 – 3( ) f  g = f (g(x)) = (2x + 1) 2 – 3(2x + 1) f  g = 4x 2 + 4x + 1 – 6x – 3 f  g = 4x 2 – 2x – 2

3. Composite Functions Example 2:Given functions and find f  g and state its domain. x x Simplify the complex fraction by multiplying the numerator and denominator by x + 1.

4. Composite Functions At first glance it might appear that the domain of f  g is the set of all real numbers except - 1.5.

5. Composite Functions Since the g function is not defined for x = - 1, neither is the f  g function. However, remember that the g function, replaced x in the f function. Therefore, the domain of f  g is: ( - , - 1.5 )  ( - 1.5, - 1 )  ( - 1,  ).

6. Composite Functions Try:Given functions and find f  g and state its domain. Its domain is: [ - 5,  ). The composite function, f  g = x.

7. Composite Functions