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y = x2 where the domain is the set of real numbers does not have an inverse, because the square root function is a one-two-two mapping (except at 0).

Any polynomial with more than one root, over the reals, has no inverse.

y = 1/x has no inverse across 0.

But it is possible to define the domain so that each of these functions has an inverse.

For example y = x2 where x is non-negative has the square root function as its inverse.

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Q: Which functions do not have an inverse?
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