Composite Functions: Examples and Domain Explanation

1. f g = f (g(x)) = (2x + 1)2 – 3(2x + 1) Composite Functions Example 1: Given functions f(x) = x2 – 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  g= f (g(x)) = (x)2 – 3(x) f  g= 4x2 + 4x + 1 – 6x – 3 f  g= 4x2 – 2x – 2

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

3. Composite Functions At first glance it might appear that the domain of f g is the set of all real numbers except - 1.5. Slide 3

4. 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,  ). Composite Functions Since the g function is not defined for x = - 1, neither is the f g function. Slide 4

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

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