query: If $ f(f(f(x)))=x$, does$ f(x)=x$ necessarily follow?
positive_passages.docid: 28925
positive_passages.text: Can the Identity Map be a repeated composition one other function?
negative_passages.docid: 41226
negative_passages.text: Find $f:f(xf(x)+f(y))=f(x)^2+y$
negative_passages.docid: 53551
negative_passages.text: $f(A\cap B)=f(A)\cap f(B)$ $\iff$ $f$ is injective.
negative_passages.docid: 72254
negative_passages.text: Is that true that not every function $f(x,y)$ can be writen as $h(x) g(y)$?
negative_passages.docid: 144222
negative_passages.text: If $f(x + 1) + f(x − 1) = f(x), \forall x \in \mathbb{R}$,then how to find $k$ such that $f(x + k) = f(x)$?
negative_passages.docid: 152782
negative_passages.text: Why does finding the $x$ that maximizes $\ln(f(x))$ is the same as finding the $x$ that maximizes $f(x)$?
negative_passages.docid: 3387
negative_passages.text: Derivative of $f(x)=|x|$
negative_passages.docid: 21954
negative_passages.text: A question about $f(x)\equiv 0$
negative_passages.docid: 103251
negative_passages.text: Solution(s) to $f(x + y) = f(x) + f(y)$ (and miscellaneous questions...)
negative_passages.docid: 132113
negative_passages.text: Does $f(x) = f(2x)$ for all real $x$, imply that $f(x)$ is a constant function?
negative_passages.docid: 26677
negative_passages.text: thoughts about $f(f(x))=e^x$
negative_passages.docid: 99827
negative_passages.text: For what values will f(x) be necessarily one-one?
negative_passages.docid: 31732
negative_passages.text: If the function $f$ satisfies the equation $f(xf(y)+x)=xy+f(x)$, find $f$
negative_passages.docid: 99906
negative_passages.text: If $f'(c)$ exists then $\lim_{x\to c} f(x)=f(c)$
negative_passages.docid: 17154
negative_passages.text: Does a non-trivial solution exist for $f'(x)=f(f(x))$?
negative_passages.docid: 97104
negative_passages.text: Proof that continuous function on $ [0, 2]$ has $f(x) = f(x-1)$ for some $ x$
negative_passages.docid: 53024
negative_passages.text: $f(x)f(1/x)=f(x)+f(1/x)$