Inverse of One-to-One Functions True or False
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Questions and Answers

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?

  • 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?

  • 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?

    <p>The function has more than one output for the same input.</p> Signup and view all the answers

    A one-to-one function always has an inverse function.

    <p>True</p> Signup and view all the answers

    The inverse of a one-to-one function is also a one-to-one function.

    <p>True</p> Signup and view all the answers

    The domain and range of a one-to-one function remain the same when finding its inverse.

    <p>True</p> Signup and view all the answers

    A one-to-one function can have more than one inverse function.

    <p>False</p> Signup and view all the answers

    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.

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