Inverses of Linear Functions

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•
Mathematics
•
8th Grade
•
Hard
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1.
FLASHCARD QUESTION
Front
What is the definition of the inverse of a function?
Back
The inverse of a function is a function that reverses the effect of the original function. If the function is denoted as f(x), its inverse is denoted as f^{-1}(x), such that f(f^{-1}(x)) = x.
2.
FLASHCARD QUESTION
Front
How do you find the inverse of a linear function?
Back
To find the inverse of a linear function, swap the x and y variables and solve for y. For example, for f(x) = mx + b, the inverse is f^{-1}(x) = (x - b)/m.
3.
FLASHCARD QUESTION
Front
What is the inverse of the relation {(-2,0), (3,4), (5,7)}?
Back
The inverse of the relation is {(0,-2), (4,3), (7,5)}.
4.
FLASHCARD QUESTION
Front
What is the inverse of the function f(x) = 4x - 5?
Back
The inverse of the function is f^{-1}(x) = \frac{x + 5}{4}.
5.
FLASHCARD QUESTION
Front
What is the general form of a linear function?
Back
The general form of a linear function is f(x) = mx + b, where m is the slope and b is the y-intercept.
6.
FLASHCARD QUESTION
Front
What does it mean for two functions to be inverses of each other?
Back
Two functions are inverses of each other if applying one function to the result of the other function returns the original input.
7.
FLASHCARD QUESTION
Front
How can you verify that two functions are inverses?
Back
To verify that two functions f(x) and g(x) are inverses, check if f(g(x)) = x and g(f(x)) = x for all x in the domain.
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