Provide an example of a function that does not have an inverse function. How do you prove that it is not a function?

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Gerardo

Mathematics

4 June, 18:27

Provide an example of a function that does not have an inverse function. How do you prove that it is not a function?

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Ashton · Answer 1

If f had an inverse, then its graph would be the reflection of the graph of f about the line y = x. The graph of f and its reflection about y = x are drawn below. Note that the reflected graph does not pass the vertical line test, so it is not the graph of a function.