Composition of Functions

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•
Mathematics
•
9th - 10th Grade
•
Hard
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1.
FLASHCARD QUESTION
Front
What is the composition of functions?
Back
The composition of functions, denoted as (f ° g)(x), is the process of applying one function to the results of another function. It means substituting the output of g(x) into f(x).
2.
FLASHCARD QUESTION
Front
If f(x) = 3x - 1 and g(x) = x² + 2, what is (f ° g)(x)?
Back
(f ° g)(x) = f(g(x)) = f(x² + 2) = 3(x² + 2) - 1 = 3x² + 6 - 1 = 3x² + 5.
3.
FLASHCARD QUESTION
Front
For f(x) = 2x² - 1, what is (f ° f)(-2)?
Back
(f ° f)(-2) = f(f(-2)) = f(2(-2)² - 1) = f(7) = 2(7)² - 1 = 97.
4.
FLASHCARD QUESTION
Front
If g(x) = 3x + 4 and h(x) = 3x - 1, find (g ∘ h)(x).
Back
(g ∘ h)(x) = g(h(x)) = g(3x - 1) = 3(3x - 1) + 4 = 9x - 3 + 4 = 9x + 1.
5.
FLASHCARD QUESTION
Front
If f(x) = 3x + 10 and g(x) = x - 2, find f(g(5)).
Back
g(5) = 5 - 2 = 3; f(g(5)) = f(3) = 3(3) + 10 = 19.
6.
FLASHCARD QUESTION
Front
What is the notation for the composition of functions?
Back
The notation for the composition of functions is (f ° g)(x), which means f(g(x)).
7.
FLASHCARD QUESTION
Front
What is the domain of a composition of functions?
Back
The domain of (f ° g)(x) is the set of all x in the domain of g such that g(x) is in the domain of f.
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