Section 8.1 Composition of Functions

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Section 8.1Composition of Functions
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• Consider the following two functions
• What is f(4)?
• What is g(8)?
• Lets 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)

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• Using the same two functions
• Lets 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)

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In your groups see if you can fill in the
following table
Inputs 1 2 3 4 5
Outputs for f 4 3 5 2 3
Outputs for g 3 4 0 2 1
Outputs for g composed with f
Outputs for f composed with g
Outputs for f composed with f
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• Using the graph find f(g(2)) and g(f(1.6))

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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) pr2. 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?

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• In your groups try problems 5, 13, and 28