Grade 12 Function Composition Worksheet
This worksheet covers key concepts and applications of function composition for Grade 12 students, including evaluating composite functions and finding domains.
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Standards
Topics
Grade 12 Function Composition
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Read each question carefully and provide your answers in the space provided. Show all your work for full credit.
Given f(x) = 2x + 3 and g(x) = x² - 1, find the following:
1. (f ∘ g)(2)
2. (g ∘ f)(-1)
Given f(x) = 3x - 2 and g(x) = x² + 4, complete the following:
3. (f ∘ g)(x) =
4. (g ∘ f)(x) =
Given f(x) = √(x - 3) and g(x) = x + 1, find the domain of (f ∘ g)(x).
6. If f(x) = 1/x and g(x) = x - 2, which of the following is the domain of (g ∘ f)(x)?
(-∞, 0) U (0, ∞)
(-∞, 2) U (2, ∞)
(-∞, ∞)
(0, ∞)
7. The order of functions in a composition does not affect the result; (f ∘ g)(x) is always equal to (g ∘ f)(x).
True
False
8. A store offers a 10% discount on all items. There is also a $5 off coupon available. Let x be the original price of an item. Write a function D(x) for the price after the discount and a function C(x) for the price after applying the coupon. Then, find and interpret (D ∘ C)(x) and (C ∘ D)(x). Which composition results in a lower final price?
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