2-6: Combinations of Functions Objective: Find and use operations on compositions of functions, and domains.

Operations on Functions Sum (f + g)(x) = Difference (f – g)(x) = Product (fg)(x) = Quotient =

Examples: f(x) = 2x2 + 7x + 3 & g(x) = x2 + 6x + 9 (f + g)(x)= 2. (f – g)(x)= 3. (fg)(x)= 4. = Find each function below, then state it’s domain.

Composition of functions The composition of the function f with the function g is: The composition of the function g with the function f is: (substitute the g function into the f) (substitute the f function into the g)

Examples Given f(x) = x + 2 & g(x) = 4 – x2 Find the composite function below, then the domain of f(x), g(x), and of each composite function: 5. 6. 7.