Evaluating Composite Functions

Flashcard
•
Mathematics
•
9th - 11th Grade
•
Medium
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14 questions
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1.
FLASHCARD QUESTION
Front
What is a composite function?
Back
A composite function is a function that is formed by combining two functions, where the output of one function becomes the input of the other. It is denoted as (f∘g)(x) = f(g(x)).
Tags
CCSS.HSF-BF.A.1C
2.
FLASHCARD QUESTION
Front
How do you evaluate a composite function?
Back
To evaluate a composite function (f∘g)(x), first evaluate g(x) and then substitute that result into f.
Tags
CCSS.HSF-BF.A.1C
3.
FLASHCARD QUESTION
Front
What is the notation for composite functions?
Back
The notation for composite functions is (f∘g)(x), which means f(g(x)).
Tags
CCSS.HSF-BF.A.1C
4.
FLASHCARD QUESTION
Front
If f(x) = 2x + 3 and g(x) = x - 1, what is (f∘g)(2)?
Back
(f∘g)(2) = f(g(2)) = f(2 - 1) = f(1) = 2(1) + 3 = 5.
Tags
CCSS.HSF-BF.A.1C
5.
FLASHCARD QUESTION
Front
What is the difference between f(g(x)) and g(f(x))?
Back
f(g(x)) means applying g first and then f, while g(f(x)) means applying f first and then g. They are generally not equal.
Tags
CCSS.HSF-BF.A.1C
6.
FLASHCARD QUESTION
Front
Given f(x) = x^2 and g(x) = 3x, find g(f(2)).
Back
g(f(2)) = g(2^2) = g(4) = 3(4) = 12.
Tags
CCSS.HSF-BF.A.1C
7.
FLASHCARD QUESTION
Front
What is the output of g(f(-10)) if f(x) = 3x + 10 and g(x) = x - 2?
Back
g(f(-10)) = g(3(-10) + 10) = g(-20) = -20 - 2 = -22. (Note: The answer is None of these as per the question.)
Tags
CCSS.HSF-BF.A.1C
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