Section 8.1 Composition of Functions

Consider the following two functions: What is f(4)? What is g(8)? Let’s say we define a function h such that h(4) = 21, what is the rule for h? In general we have h(x) = g(f(x)) Find h(2) and h(6) What if we have k(x) = f (g(x)) Find k(2) and k(6)

Using the same two functions: Let’s find algebraic rules for h(x) = g(f(x)) and k(x) = f (g(x)) Using your new functions find h(2), h(6), k(2) and k(6)

In your groups see if you can fill in the following table Inputs 1 2 3 4 5 Outputs for f Outputs for g Outputs for g composed with f Outputs for f composed with g Outputs for f composed with f

Using the graph find f(g(2)) and g(f(1.6))

Example Suppose that oil is leaking out of a damaged tanker. The oil is forming a circular-shaped slick on the surface of the water. Suppose that the radius t hours after the leak began is given by r = f(t) = 300t meters. Note that the area of a circle is a function of its radius given by A = g(r) = πr2. What does g composed with f represent? Find a formula for the area of the slick t hours after it spilled. For how many hours has it been leaking to have an area of 10,000,000 square meters?

In your groups try problems 5, 13, and 28