query: Is there a function so that $f(f(x))=1/x$?
positive_passages.docid: 24306
positive_passages.text: Is there a continuous function $f(x)$ such that the inverse function is $1/f(x)$?
negative_passages.docid: 153510
negative_passages.text: Questions about the existence of a function
negative_passages.docid: 121455
negative_passages.text: $f(x)$ if $f(xy)=f(x) +f(y) +\frac{x+y-1}{xy}$
negative_passages.docid: 138481
negative_passages.text: $f(x)=x/1$ is not injective?
negative_passages.docid: 28927
negative_passages.text: IMO 1987 - function such that $f(f(n))=n+1987$
negative_passages.docid: 3518
negative_passages.text: Proving $f(x)=1/x$ on $(0,1 )$ is not uniformly continuous
negative_passages.docid: 99917
negative_passages.text: What function satisfies $F'(x) = F(2x)$?
negative_passages.docid: 55175
negative_passages.text: Is the function $f(x) = x^2 - 2x$ one-to-one?
negative_passages.docid: 111990
negative_passages.text: Continuous function from $(0, 1]$ onto $(0, 1)$?
negative_passages.docid: 156778
negative_passages.text: Finding functions satisfying $f(f(x))+f(x)+x=0$
negative_passages.docid: 124894
negative_passages.text: Looking for a function such that...
negative_passages.docid: 151958
negative_passages.text: How to show $f'(0)$ exist and is equal to $1$?
negative_passages.docid: 68774
negative_passages.text: Proving that $f(x)$ is less than or equal to $1+\pi/4$
negative_passages.docid: 77074
negative_passages.text: If $ f(f(f(x)))=x$, does$ f(x)=x$ necessarily follow?
negative_passages.docid: 106830
negative_passages.text: are $f(f(x))=f(x)$ and $f(x)=x$ equivalent?
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: 81799
negative_passages.text: Examples of functions where $f(ab)=f(a)+f(b)$