
Composition of Functions with Graphs and Tables
Flashcard
•
Mathematics
•
9th - 11th Grade
•
Practice Problem
•
Hard
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1.
FLASHCARD QUESTION
Front
What is the composition of functions?
Back
The composition of functions is the process of applying one function to the results of another function. If f and g are two functions, the composition is denoted as (f ∘ g)(x) = f(g(x)).
2.
FLASHCARD QUESTION
Front
How do you evaluate a composition of functions?
Back
To evaluate a composition of functions, substitute the input value into the innermost function and then use the result as the input for the outer function.
3.
FLASHCARD QUESTION
Front
What is the notation for the composition of functions?
Back
The notation for the composition of functions is f(g(x)), which means 'apply g to x, then apply f to the result of g(x)'.
4.
FLASHCARD QUESTION
Front
If f(x) = 2x + 3 and g(x) = x - 1, what is f(g(4))?
Back
f(g(4)) = f(4 - 1) = f(3) = 2(3) + 3 = 9.
5.
FLASHCARD QUESTION
Front
What is the value of h(g(-3)) if h(x) = x and g(x) = x?
Back
h(g(-3)) = h(-3) = -3.
6.
FLASHCARD QUESTION
Front
How do you find f(f(x)) for a given function f?
Back
To find f(f(x)), substitute f(x) into itself. For example, if f(x) = 2x, then f(f(x)) = f(2x) = 2(2x) = 4x.
7.
FLASHCARD QUESTION
Front
What is the significance of the order of functions in composition?
Back
The order of functions in composition matters because (f ∘ g)(x) is generally not equal to (g ∘ f)(x). The output of one function becomes the input of the next.
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