I have come across a problem which asks to find $f(x)$ such that $f(f(x))=-x$. Nothing I can find has anything pertaining to the composition of two identical functions. Is there a way that I can dissect this in order to help in finding a possible $f(x)$?
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I don't think it is possible if
Through late night serendipity and later verification, I have found that $f(x)=ix$ works for all real numbers.