Unit 2B Day 2 Composition of Functions
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•
Mathematics
•
11th Grade
•
Hard
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1.
FLASHCARD QUESTION
Front
What is the composition of functions?
Back
The composition of functions is a process where one function is applied to the result of another function, denoted as (f ° g)(x) = f(g(x)).
2.
FLASHCARD QUESTION
Front
How do you calculate (f ° f)(x) for a function f(x)?
Back
To calculate (f ° f)(x), you substitute f(x) into itself, meaning you replace x in f(x) with f(x).
3.
FLASHCARD QUESTION
Front
Given f(x) = x^2 - 1, what is f(3)?
Back
f(3) = 3^2 - 1 = 9 - 1 = 8.
4.
FLASHCARD QUESTION
Front
What is the formula for the composition of two functions f(x) and g(x)?
Back
The formula for the composition of two functions is (f ° g)(x) = f(g(x)).
5.
FLASHCARD QUESTION
Front
If f(x) = 2x^2 - 1, what is f(-2)?
Back
f(-2) = 2(-2)^2 - 1 = 2(4) - 1 = 8 - 1 = 7.
6.
FLASHCARD QUESTION
Front
What does g(f(x)) represent in function composition?
Back
g(f(x)) represents the function g applied to the output of the function f at x.
7.
FLASHCARD QUESTION
Front
How do you find the value of (g ° f)(-2) if g(x) = x + 3 and f(x) = 2x^2 - 1?
Back
First, find f(-2) = 7, then find g(7) = 7 + 3 = 10, so (g ° f)(-2) = 10.
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