Functions and compositions

Flashcard
•
Mathematics
•
11th Grade
•
Hard
+1
Standards-aligned
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15 questions
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1.
FLASHCARD QUESTION
Front
What is a function?
Back
A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output.
Tags
CCSS.8.F.A.1
2.
FLASHCARD QUESTION
Front
What is function composition?
Back
Function composition is the process of applying one function to the results of another function. If f and g are functions, then the composition of f and g is denoted as f(g(x)).
Tags
CCSS.HSF-BF.A.1C
3.
FLASHCARD QUESTION
Front
How do you find f(g(x))?
Back
To find f(g(x)), first evaluate g(x) for a given x, then substitute that result into f.
Tags
CCSS.HSF-BF.A.1C
4.
FLASHCARD QUESTION
Front
What is the inverse of a function?
Back
The inverse of a function f(x) is a function that reverses the effect of f. If f(x) = y, then f^(-1)(y) = x.
Tags
CCSS.HSF-BF.B.4A
5.
FLASHCARD QUESTION
Front
How do you find the inverse of f(x) = 1/4x - 7?
Back
To find the inverse, swap x and y, then solve for y: y = 1/4x - 7 becomes x = 1/4y - 7, leading to f^(-1)(x) = 4x + 28.
Tags
CCSS.HSF-BF.B.4A
6.
FLASHCARD QUESTION
Front
What is the sum of two functions?
Back
The sum of two functions f and g, denoted (f + g)(x), is defined as f(x) + g(x).
Tags
CCSS.HSF-BF.A.1B
7.
FLASHCARD QUESTION
Front
Given f(x) = 3x^2 + 7x and g(x) = 2x^2 - x - 1, find (f + g)(x).
Back
(f + g)(x) = 5x^2 + 6x - 1.
Tags
CCSS.HSF-BF.A.1B
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