query: Find a function that matches the following conditions.
positive_passages.docid: 145919
positive_passages.text: If $f: \Bbb{R}\rightarrow\Bbb{R}$ is continuous at $0$ and $f(x)=f(2x)$ for each $x\in\Bbb{R}$ then $f$ is constant.
negative_passages.docid: 32432
negative_passages.text: Strategies to find the set of functions $f:\mathbb R\to\mathbb R$ satisfing the functional equation: $f(x^3)+f(y^3)=(x+y)(f(x^2)+f(y^2)-f(xy))$
negative_passages.docid: 29647
negative_passages.text: Do there exist functions satisfying $f(x+y)=f(x)+f(y)$ that aren't linear?
negative_passages.docid: 409
negative_passages.text: functions satisfying $f(x - y) = f(x) f(y) - f(a - x) f(a + y)$ and $f(0)=1$
negative_passages.docid: 148470
negative_passages.text: bound of the function
negative_passages.docid: 37736
negative_passages.text: How to find a function in $ L_{2}(0,\infty)$ but not $L_{q}(0,\infty)$, $q\neq 2 $
negative_passages.docid: 56127
negative_passages.text: Prove a function is constant under certain conditions
negative_passages.docid: 51019
negative_passages.text: Polynomial problem with two conditions
negative_passages.docid: 118565
negative_passages.text: Find a function value given 2 points
negative_passages.docid: 89883
negative_passages.text: Find the leading order uniform approximation when the conditions are not $0<x<1$
negative_passages.docid: 56135
negative_passages.text: Find all permutations with a condition
negative_passages.docid: 99917
negative_passages.text: What function satisfies $F'(x) = F(2x)$?
negative_passages.docid: 140978
negative_passages.text: Real domain and range function to find all functions with nonzero x.
negative_passages.docid: 153510
negative_passages.text: Questions about the existence of a function
negative_passages.docid: 110704
negative_passages.text: Find all functions $f$ such that $f(x)+f(\frac{1}{1-x})=x$
negative_passages.docid: 42218
negative_passages.text: How to find out the following function f which is a function of r?
negative_passages.docid: 115943
negative_passages.text: If condition with 2 different values within certain range (boundary)