Combination & Composition of Functions Flashcard

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•
Mathematics
•
12th Grade
•
Hard
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1.
FLASHCARD QUESTION
Front
Define combination of functions.
Back
The combination of functions refers to the process of adding, subtracting, multiplying, or dividing two functions to create a new function.
2.
FLASHCARD QUESTION
Front
What is composition of functions?
Back
Composition of functions is the operation where one function is applied to the result of another function, denoted as (f ∘ g)(x) = f(g(x)).
3.
FLASHCARD QUESTION
Front
If f(x) = x^2 and g(x) = x + 1, what is (f + g)(x)?
Back
(f + g)(x) = x^2 + (x + 1) = x^2 + x + 1.
4.
FLASHCARD QUESTION
Front
Calculate (f - g)(x) if f(x) = 2x + 3 and g(x) = x - 1.
Back
(f - g)(x) = (2x + 3) - (x - 1) = x + 4.
5.
FLASHCARD QUESTION
Front
What is the formula for (f * g)(x)?
Back
(f * g)(x) = f(x) * g(x), which means multiplying the outputs of f and g for the same input x.
6.
FLASHCARD QUESTION
Front
If f(x) = 3x and g(x) = 2x^2, find (f / g)(x).
Back
(f / g)(x) = 3x / (2x^2) = 3 / (2x) for x ≠ 0.
7.
FLASHCARD QUESTION
Front
Find f(g(2)) if f(x) = x^2 and g(x) = 3x + 1.
Back
g(2) = 3(2) + 1 = 7; then f(g(2)) = f(7) = 7^2 = 49.
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