Function Composition Exploration
This worksheet focuses on understanding and applying function composition with various types of functions, suitable for Grade 11 mathematics students.
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Function Composition Exploration
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Read each question carefully and provide clear, complete answers. Show all your work where applicable.
1. The notation (f ∘ g)(x) represents the of functions f and g.
2. To evaluate (f ∘ g)(x), you first apply the function to x, and then apply the function to the result.
3. The domain of (f ∘ g)(x) consists of all x in the domain of g such that g(x) is in the domain of .
Given f(x) = 2x + 3 and g(x) = x² - 1, find the following:
4. (f ∘ g)(2)
5. (g ∘ f)(-1)
6. (f ∘ f)(0)
Given f(x) = 3x - 2 and g(x) = x + 5, which of the following is (f ∘ g)(x)?
3x + 13
3x + 3
3x + 7
3x - 7
Given h(x) = x² and k(x) = √x, which of the following is (k ∘ h)(x)?
x
x²
|x|
√x
Given f(x) = 1/(x-2) and g(x) = √x, find the composite function and its domain.
7. Find (f ∘ g)(x).
8. State the domain of (f ∘ g)(x).
For any two functions f and g, (f ∘ g)(x) is always equal to (g ∘ f)(x).
True
False
If f(x) = x and g(x) = x², then (f ∘ g)(x) = x².
True
False
A store offers a 20% discount on all items. On top of that, a coupon gives an additional $10 off. Let x be the original price of an item.
9. Write a function D(x) for the price after the 20% discount.
10. Write a function C(x) for the price after the $10 coupon.
11. Find (C ∘ D)(x) and explain what it represents in this context.
12. Find (D ∘ C)(x) and explain what it represents in this context.
13. Which order of applying the discounts results in a lower final price for an item that originally costs $100? Justify your answer.