Day 66 Alg 2 Composition of Functions

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Mathematics
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9th - 12th Grade
•
Hard
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1.
FLASHCARD QUESTION
Front
What is a function composition?
Back
Function composition is the process of applying one function to the results of another function. If you have two functions, f(x) and g(x), the composition is denoted as (g ∘ f)(x) = g(f(x)).
2.
FLASHCARD QUESTION
Front
If f(x) = 2x + 3 and g(x) = x^2, what is (g ∘ f)(x)?
Back
(g ∘ f)(x) = g(f(x)) = g(2x + 3) = (2x + 3)^2 = 4x^2 + 12x + 9.
3.
FLASHCARD QUESTION
Front
What is the notation for function composition?
Back
The notation for function composition is (g ∘ f)(x), which means g(f(x)).
4.
FLASHCARD QUESTION
Front
If f(x) = x^2 and g(x) = 3x + 1, find (f ∘ g)(2).
Back
(f ∘ g)(2) = f(g(2)) = f(3(2) + 1) = f(7) = 7^2 = 49.
5.
FLASHCARD QUESTION
Front
What is the domain of a composite function?
Back
The domain of a composite function (g ∘ f)(x) is the set of all x in the domain of f such that f(x) is in the domain of g.
6.
FLASHCARD QUESTION
Front
If f(x) = x - 1 and g(x) = 2x, find (g ∘ f)(x).
Back
(g ∘ f)(x) = g(f(x)) = g(x - 1) = 2(x - 1) = 2x - 2.
7.
FLASHCARD QUESTION
Front
What is the range of a function?
Back
The range of a function is the set of all possible output values (y-values) that the function can produce.
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