query: Find all functions $ f: (0, \infty) \mapsto (0, \infty)$
positive_passages.docid: 146347
positive_passages.text: An imo shortlist algebra question
negative_passages.docid: 46156
negative_passages.text: How to find $\lim_{x \to \infty} [x]/x$?
negative_passages.docid: 62966
negative_passages.text: Find all functions $f(x)$ such that $f\left(x^2+f(y)\right)$=$y+(f(x))^2$
negative_passages.docid: 122329
negative_passages.text: Determine all functions $f(x)$ such that $f(f(x+y))=f(x)+f(y)$
negative_passages.docid: 23186
negative_passages.text: $f: \mathbb{R^2} \to \mathbb{R}$ a $C^\infty$ function such that $f(x,0)=f(0,y)=0$ then exists $g$ such that $f(x,y)=xy\, g(x,y)$
negative_passages.docid: 11453
negative_passages.text: Find a real function $f:\mathbb{R}\to\mathbb{R}$ such that $f(f(x)) = -x$?
negative_passages.docid: 26754
negative_passages.text: Find all continuous functions satisfying $\int_0^xf=(f(x))^2+C$ for some constant $C \neq 0$.
negative_passages.docid: 109942
negative_passages.text: Find continuous functions such that $f(x+y)+f(x-y)=2[f(x)+f(y)]$
negative_passages.docid: 112089
negative_passages.text: Find the Maclaurin series of f(x)
negative_passages.docid: 150896
negative_passages.text: Show that $\lim_{p \to \infty} \| f \|_p = \| f \|_\infty$
negative_passages.docid: 50552
negative_passages.text: find functions that $f(m+k)=f(mk-n)$
negative_passages.docid: 13116
negative_passages.text: How to write a pattern that matches all functions
negative_passages.docid: 44370
negative_passages.text: If $f(x)\to 0$ as $x\to\infty$ and $f''$ is bounded, show that $f'(x)\to0$ as $x\to\infty$
negative_passages.docid: 136655
negative_passages.text: Find the range of the given function $f$
negative_passages.docid: 124971
negative_passages.text: Find all holomorphic functions with $\Re(f(x+iy))=2xy$
negative_passages.docid: 28949
negative_passages.text: Prove $f(x) = 0 $for all $x \in [0, \infty)$ when $|f'(x)| \leq |f(x)|$
negative_passages.docid: 13732
negative_passages.text: $||f||_p\to ||f||_\infty$ under general assumptions