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.
Includes
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?