composition of functions+function operations
Flashcard
•
Mathematics
•
10th - 12th Grade
•
Practice Problem
•
Hard
Standards-aligned
Wayground Content
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15 questions
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1.
FLASHCARD QUESTION
Front
What is the composition of functions?
Back
The composition of functions is a way to combine two functions, where the output of one function becomes the input of another. It is denoted as (f ∘ g)(x) = f(g(x)).
Tags
CCSS.HSF-BF.A.1C
2.
FLASHCARD QUESTION
Front
If f(x) = 2x and g(x) = x + 3, what is (f ∘ g)(2)?
Back
(f ∘ g)(2) = f(g(2)) = f(2 + 3) = f(5) = 2(5) = 10.
Tags
CCSS.HSF-BF.A.1C
3.
FLASHCARD QUESTION
Front
Define the term 'function operation'.
Back
Function operations refer to the various ways functions can be combined or manipulated, including addition, subtraction, multiplication, division, and composition.
Tags
CCSS.HSF-BF.A.1B
4.
FLASHCARD QUESTION
Front
What is the result of (g ∘ f)(x) if f(x) = x^2 and g(x) = 3x?
Back
(g ∘ f)(x) = g(f(x)) = g(x^2) = 3(x^2) = 3x^2.
Tags
CCSS.HSF-BF.A.1C
5.
FLASHCARD QUESTION
Front
If f(x) = x + 1 and g(x) = 2x, find (f + g)(x).
Back
(f + g)(x) = f(x) + g(x) = (x + 1) + (2x) = 3x + 1.
Tags
CCSS.HSF-BF.A.1B
6.
FLASHCARD QUESTION
Front
What is the formula for the composition of two functions f and g?
Back
The formula for the composition of two functions is (f ∘ g)(x) = f(g(x)).
Tags
CCSS.HSF-BF.A.1C
7.
FLASHCARD QUESTION
Front
If f(x) = x^2 and g(x) = x + 1, what is (f ∘ g)(-1)?
Back
(f ∘ g)(-1) = f(g(-1)) = f(-1 + 1) = f(0) = 0^2 = 0.
Tags
CCSS.HSF-BF.A.1C
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