TITLE: Given $f(f(x))$ can we find $f(x)$?
QUESTION [26 upvotes]: Given $f(f(x))=x+2$ does it necessarily follow that $f(x)=x+1$? This question comes from a precalculus algebra student.

REPLY [13 votes]: Answering the question in the topic: definitely not for all $f$.  Consider $f(f(x))) = x$; is $f(x) = x$ or $f(x) = -x$?