query: Strictly monotone functions such that $x= f(\frac{x^2}{f(x)})$
positive_passages.docid: 17119
positive_passages.text: Find all strictly monotone $f:(0,+\infty) \to (0, +\infty)$ such that $f(\frac{x^2}{f(x)})=x.$
negative_passages.docid: 153510
negative_passages.text: Questions about the existence of a function
negative_passages.docid: 18082
negative_passages.text: A continuous function that attains neither its minimum nor its maximum at any open interval is monotone
negative_passages.docid: 28011
negative_passages.text: Does there exists an entire function such that for each $|z|>C$ for some constant $C$, $|f(z)|=|z|+1$?
negative_passages.docid: 122758
negative_passages.text: Are Monotone functions Borel Measurable?
negative_passages.docid: 99894
negative_passages.text: Does there exists an entire function $f$ such that $f(0)=1$ and $|f(z)|\leq \frac{1}{|z|} $ for all $|z|\geq 5$?
negative_passages.docid: 17343
negative_passages.text: Function on $[a,b]$ that satisfies a Hölder condition of order $\alpha > 1 $ is constant
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: 157731
negative_passages.text: Show that one-sided limits always exist for a monotone function (on an interval)
negative_passages.docid: 72769
negative_passages.text: How find this function $xf(x^2)=f(x),x>0$
negative_passages.docid: 92638
negative_passages.text: Approximation of measurable function by simple functions
negative_passages.docid: 74810
negative_passages.text: A function $f$ such that $f' = 0$ when $x < 0$ and $f' = 1$ when $x \geq 0$?
negative_passages.docid: 63701
negative_passages.text: An example of a regular function over an open set
negative_passages.docid: 53738
negative_passages.text: Monotone functions and continuity
negative_passages.docid: 84317
negative_passages.text: Iterated self-composition of arbitrary function
negative_passages.docid: 152563
negative_passages.text: Set of discontinuity of monotone function is countable
negative_passages.docid: 31308
negative_passages.text: Does there exist some strictly positive function such that both the derivative and second derivative are strictly negative?