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I know that functions can be their own inverse such as $f(x)=x$ however I thought there were only two $f(x)=x$ and $f(x)=-x$. Is there more?

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marked as duplicate by Simon S, Community Jul 13 '15 at 16:56

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There are an infinite number of these functions. Consider $f(x)=a/x$ for some $a$. There are also many many others that are not of this form. Even if you restrict to continuous functions, there are infinitely many.

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