Inverse Functions

Flashcard
•
Mathematics
•
11th Grade - University
•
Hard
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1.
FLASHCARD QUESTION
Front
What is an inverse function?
Back
An inverse function reverses the operation of the original function. If f(x) takes an input x and produces an output y, then the inverse function f⁻¹(y) takes y and produces x.
2.
FLASHCARD QUESTION
Front
How do you find the inverse of a function algebraically?
Back
To find the inverse of a function, replace f(x) with y, swap x and y, and then solve for y. The resulting equation is the inverse function.
3.
FLASHCARD QUESTION
Front
What is the relationship between a function and its inverse?
Back
A function and its inverse are reflections of each other over the line y = x.
4.
FLASHCARD QUESTION
Front
If f(x) = 2x + 3, what is f⁻¹(x)?
Back
f⁻¹(x) = (x - 3)/2.
5.
FLASHCARD QUESTION
Front
What does it mean for two functions to be inverses of each other?
Back
If f and g are inverse functions, then f(g(x)) = x and g(f(x)) = x for all x in the domain.
6.
FLASHCARD QUESTION
Front
What is the graphical representation of an inverse function?
Back
The graph of an inverse function is obtained by reflecting the graph of the original function over the line y = x.
7.
FLASHCARD QUESTION
Front
How can you verify if two functions are inverses?
Back
To verify if two functions f and g are inverses, check if f(g(x)) = x and g(f(x)) = x for all x in their domains.
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