Define composition of functions.
Composition of Functions

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Mathematics
•
11th Grade
•
Hard
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1.
FLASHCARD QUESTION
Front
Back
The composition of functions is a process where one function is applied to the result of another function. If \( f(x) \) and \( g(x) \) are two functions, the composition is denoted as \( (f \circ g)(x) = f(g(x)) \).
2.
FLASHCARD QUESTION
Front
What is the formula for finding \( f(g(x)) \) if \( f(x) = 2x + 3 \) and \( g(x) = -3x - 4 \)?
Back
To find \( f(g(x)) \), substitute \( g(x) \) into \( f(x) \): \( f(g(x)) = f(-3x - 4) = 2(-3x - 4) + 3 = -6x - 8 + 3 = -6x - 5 \).
3.
FLASHCARD QUESTION
Front
How do you find \( f(g(x)) \) for \( f(x) = \frac{1}{x} \) and \( g(x) = 3x + 2 \)?
Back
Substitute \( g(x) \) into \( f(x) \): \( f(g(x)) = f(3x + 2) = \frac{1}{3x + 2} \).
4.
FLASHCARD QUESTION
Front
What is the result of \( (f \circ g)(-1) \) if \( f(x) = x^2 \) and \( g(x) = \frac{1}{x^2} \)?
Back
Calculate \( g(-1) = \frac{1}{(-1)^2} = 1 \) and then \( f(1) = 1^2 = 1 \). Thus, \( (f \circ g)(-1) = 1 \).
5.
FLASHCARD QUESTION
Front
Find \( (g \circ f)(x) \) for \( f(x) = \frac{1}{x} \) and \( g(x) = 3x + 2 \).
Back
Substitute \( f(x) \) into \( g(x) \): \( g(f(x)) = g\left(\frac{1}{x}\right) = 3\left(\frac{1}{x}\right) + 2 = \frac{3}{x} + 2 \).
6.
FLASHCARD QUESTION
Front
What is the composition \( g(f(x)) \) if \( f(x) = 2x \) and \( g(x) = 2x^2 - 1 \)?
Back
Substituting \( f(x) \) into \( g(x) \): \( g(f(x)) = g(2x) = 2(2x)^2 - 1 = 8x^2 - 1 \).
7.
FLASHCARD QUESTION
Front
Explain the notation \( f \circ g \).
Back
The notation \( f \circ g \) represents the composition of functions \( f \) and \( g \), meaning \( f(g(x)) \).
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