Interpreting Composite Functions

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•
Mathematics
•
10th Grade
•
Hard
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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 another. It is denoted as (f ∘ g)(x) = f(g(x)).
2.
FLASHCARD QUESTION
Front
How do you denote the composition of two functions f and g?
Back
The composition of two functions f and g is denoted as (f ∘ g)(x).
3.
FLASHCARD QUESTION
Front
What is the correct setup for (g ∘ f)(x) given f(x) = 3x - 2 and g(x) = 8 - 7x?
Back
The correct setup is g(f(x)) = 8 - 7(3x - 2).
4.
FLASHCARD QUESTION
Front
What do you type into DESMOS for (f ∘ g)(7) if f(x) = 3x - 2 and g(x) = 8 - 7x?
Back
You type f(g(7)).
5.
FLASHCARD QUESTION
Front
What is the difference between (f + g)(x) and (f ∘ g)(x)?
Back
(f + g)(x) is the sum of the functions evaluated at x, while (f ∘ g)(x) is the composition of f and g, meaning you first apply g to x and then apply f to the result.
6.
FLASHCARD QUESTION
Front
What is the correct setup for (f - g)(x) given f(x) = 3x - 2 and g(x) = 8 - 7x?
Back
The correct setup is (f - g)(x) = (3x - 2) - (8 - 7x).
7.
FLASHCARD QUESTION
Front
How do you evaluate (f ∘ g ∘ h)(7) using functions f, g, and h?
Back
You evaluate it as h(g(f(7))).
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