8 Questions
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.
What happens to the domain and range when finding the inverse of a one-to-one function?
The domain and range switch places.
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.
If a function does not have an inverse, what is a possible reason for this?
The function has more than one output for the same input.
A one-to-one function always has an inverse function.
True
The inverse of a one-to-one function is also a one-to-one function.
True
The domain and range of a one-to-one function remain the same when finding its inverse.
True
A one-to-one function can have more than one inverse function.
False
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.
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.
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