composition of functions+function operations

Flashcard
•
Mathematics
•
10th - 12th Grade
•
Hard
+1
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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) = 2x^2 - 1, what is g(f(x))?
Back
g(f(x)) = g(2x) = 2(2x)^2 - 1 = 8x^2 - 1.
Tags
CCSS.HSF-BF.A.1C
3.
FLASHCARD QUESTION
Front
What is the formula for multiplying two functions f(x) and g(x)?
Back
The product of two functions is given by (f ⋅ g)(x) = f(x) * g(x).
Tags
CCSS.HSF-BF.A.1B
4.
FLASHCARD QUESTION
Front
If f(x) = 2x + 3 and g(x) = -3x - 4, what is f(x) * g(x)?
Back
f(x) * g(x) = (2x + 3)(-3x - 4) = -6x^2 - 17x - 12.
Tags
CCSS.HSF-BF.A.1B
5.
FLASHCARD QUESTION
Front
What is the value of f(g(3)) if f(x) = 2x and g(x) = 2x^2 - 1?
Back
f(g(3)) = f(2(3)^2 - 1) = f(17) = 2(17) = 34.
Tags
CCSS.HSF-BF.A.1C
6.
FLASHCARD QUESTION
Front
What is the sum of two functions f(x) and g(x)?
Back
The sum of two functions is given by (f + g)(x) = f(x) + g(x).
Tags
CCSS.HSF-BF.A.1B
7.
FLASHCARD QUESTION
Front
If f(x) = 9 - 3x and g(x) = 5x - 7, what is f(x) + g(x)?
Back
f(x) + g(x) = (9 - 3x) + (5x - 7) = 2x + 2.
Tags
CCSS.HSF-BF.A.1B
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