Composition of Functions

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•
Mathematics
•
9th - 12th 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
If f(x) = 2x + 3 and g(x) = x - 1, what is g(f(2))?
Back
g(f(2)) = g(2*2 + 3) = g(7) = 7 - 1 = 6.
3.
FLASHCARD QUESTION
Front
What does it mean to evaluate a function?
Back
To evaluate a function means to find the output value of the function for a given input value.
4.
FLASHCARD QUESTION
Front
If f(x) = x^2 and g(x) = 3x, what is (f ° g)(x)?
Back
(f ° g)(x) = f(g(x)) = f(3x) = (3x)^2 = 9x^2.
5.
FLASHCARD QUESTION
Front
What is the formula for finding g(h(x)) if g(x) = 3x + 4 and h(x) = 3x - 1?
Back
g(h(x)) = g(3x - 1) = 3(3x - 1) + 4 = 9x - 3 + 4 = 9x + 1.
6.
FLASHCARD QUESTION
Front
How do you find f(-1) if f(x) = 2x^2 + 5x - 17?
Back
f(-1) = 2(-1)^2 + 5(-1) - 17 = 2 - 5 - 17 = -20.
7.
FLASHCARD QUESTION
Front
What is the result of (f ° g)(x) if f(x) = x - 5 and g(x) = 3x^2 - 1?
Back
(f ° g)(x) = f(g(x)) = f(3x^2 - 1) = (3x^2 - 1) - 5 = 3x^2 - 6.
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