# How many different functions are there that are equal to their own inverse? [duplicate]

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?
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.