query: $f:\mathbb R\rightarrow [0,\infty )$ is continuous such that $g(x)={(f(x))}^2$ is uniformly continuous .
positive_passages.docid: 24017
positive_passages.text: Let $f: \Bbb R \to [0,\infty)$ be a continuous function such that $g(x)=(f(x))^2$ is uniformly continuous. Which of the following is always true?
negative_passages.docid: 129073
negative_passages.text: If $f'$ is bounded, then $f$ is uniformly continuous
negative_passages.docid: 90565
negative_passages.text: If $f:[0,1] \rightarrow \mathbb{R}$ is continuous function such that $f(0)=f(1)$ then there exists $ x\in [0,1]$ such that $f(x) = f(x+\frac{1}{n})$.
negative_passages.docid: 1986
negative_passages.text: Show $1/(1+ x^2)$ is uniformly continuous on $\Bbb R$.
negative_passages.docid: 47419
negative_passages.text: Asymptotics of uniformly continuous functions over $\mathbb R$
negative_passages.docid: 11158
negative_passages.text: Proof that a continuous function with $f(x) = f(x^2)$ is constant.
negative_passages.docid: 104044
negative_passages.text: Prove continuous functions $f$ and $g$ are equal
negative_passages.docid: 125024
negative_passages.text: Is this function uniformly continuous?
negative_passages.docid: 15579
negative_passages.text: Show that $f$ is uniformly continuous if limit exists
negative_passages.docid: 129856
negative_passages.text: Show that $f(x)=\frac{x}{1+|x|}$ is uniformly continuous.
negative_passages.docid: 28730
negative_passages.text: product of two uniformly continuous functions is uniformly continuous
negative_passages.docid: 58597
negative_passages.text: A characterization of functions from $\mathbb R^n$ to $\mathbb R^m$ which are continuous
negative_passages.docid: 93021
negative_passages.text: $f:X\longrightarrow\mathbb{R}$ is continuous iff $\{x\in X:f(x)\geq\alpha\}$ and $\{x\in X:f(x)\leq\alpha\}$ are closed $\forall\alpha\in\mathbb{R}$
negative_passages.docid: 93461
negative_passages.text: Suppose that $f:\Bbb R\to \Bbb R$ is continuous and that $f(x)\to 0$ as $x\to \pm\infty.$Prove that $f$ is uniformly continuous.
negative_passages.docid: 15284
negative_passages.text: $f$ defined on $[1,\infty )$ is uniformly continuous. Then $\exists M>0$ s.t. $\frac{|f(x)|}{x}\le M$ for $x\ge 1$.
negative_passages.docid: 9614
negative_passages.text: How does the existence of a limit imply that a function is uniformly continuous
negative_passages.docid: 51247
negative_passages.text: $f$ be a continuous function maps Cauchy into Cauchy. Is $f$ uniformly continuous?