Podcast
Questions and Answers
Which of the following statements is true about the inverse of a one-to-one function?
Which of the following statements is true about the inverse of a one-to-one function?
- The inverse of a one-to-one function is also a function. (correct)
- The inverse of a one-to-one function is not a function.
- The inverse of a one-to-one function always has multiple outputs for the same input.
- The inverse of a one-to-one function has the same domain as the original function.
What happens to the domain and range when finding the inverse of a one-to-one function?
What happens to the domain and range when finding the inverse of a one-to-one function?
- The domain and range switch places. (correct)
- The domain becomes the range and the range becomes the domain.
- The inverse has no effect on the domain and range.
- The domain and range remain the same.
What is the relationship between a one-to-one function and its inverse?
What is the relationship between a one-to-one function and its inverse?
- A one-to-one function and its inverse are reflections over the line y = x. (correct)
- A one-to-one function and its inverse are always equal.
- A one-to-one function and its inverse always have the same graph.
- A one-to-one function and its inverse have no relationship.
If a function does not have an inverse, what is a possible reason for this?
If a function does not have an inverse, what is a possible reason for this?
A one-to-one function always has an inverse function.
A one-to-one function always has an inverse function.
The inverse of a one-to-one function is also a one-to-one function.
The inverse of a one-to-one function is also a one-to-one function.
The domain and range of a one-to-one function remain the same when finding its inverse.
The domain and range of a one-to-one function remain the same when finding its inverse.
A one-to-one function can have more than one inverse function.
A one-to-one function can have more than one inverse function.
Study Notes
Inverse of a One-to-One Function
- A one-to-one function always has an inverse function.
- The inverse of a one-to-one function is also a one-to-one function.
- When finding the inverse of a one-to-one function, the domain and range are swapped, meaning the domain of the original function becomes the range of the inverse function, and vice versa.
Why a Function May Not Have an Inverse
- If a function does not have an inverse, a possible reason is that it is not one-to-one.
Important Note
- A one-to-one function cannot have more than one inverse function.
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Description
Test your knowledge about the inverse of one-to-one functions with this true or false quiz. Explore the relationship between a one-to-one function and its inverse, and understand what happens to the domain and range when finding the inverse of a one-to-one function.
