query: Find all continuous functions $f:\mathbb R\to\mathbb R$ such that $f(f(x))=e^{x}$
positive_passages.docid: 26677
positive_passages.text: thoughts about $f(f(x))=e^x$
negative_passages.docid: 44670
negative_passages.text: Find all functions $f: \mathbb Z \to \mathbb Z$ such that $f(x+y)=f(x)+f(y)$
negative_passages.docid: 83326
negative_passages.text: $f:\mathbb R\to\mathbb R$ continuous function. Which of the following sets can not be image of $(0,1]$ under $f$?
negative_passages.docid: 2142
negative_passages.text: Finding a set of continuous functions with a certain property 2
negative_passages.docid: 131992
negative_passages.text: A problem on continuous functions
negative_passages.docid: 41201
negative_passages.text: How prove there is no continuous functions $f:[0,1]\to \mathbb R$, such that $f(x)+f(x^2)=x$.
negative_passages.docid: 52380
negative_passages.text: How to prove the function $e^x$ is continous for all real numbers
negative_passages.docid: 143354
negative_passages.text: Prove that there exists $c\in\mathbb{R}$ such that $f'(c)=f(c)$
negative_passages.docid: 103019
negative_passages.text: Find all functoins $f: \mathbb R \rightarrow \mathbb R$ such that $\forall x,y \in \mathbb R f(xy+f(x))=xf(y)+f(x)$
negative_passages.docid: 66406
negative_passages.text: How to calculate $f(x)$ in $f(f(x)) = e^x$?
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: 151427
negative_passages.text: f, g continuous for all rationals follow by continuous on all reals?
negative_passages.docid: 111990
negative_passages.text: Continuous function from $(0, 1]$ onto $(0, 1)$?
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: 62723
negative_passages.text: If $f\colon \mathbb{R} \to \mathbb{R}$ is such that $f (x + y) = f (x) f (y)$ and continuous at $0$, then continuous everywhere
negative_passages.docid: 22303
negative_passages.text: How do I prove that $f(x)f(y)=f(x+y)$ implies that $f(x)=e^{cx}$, assuming f is continuous and not zero?
negative_passages.docid: 92089
negative_passages.text: If $f:[a,b]\to \mathbb{R}$ is continuous and nonnegative and $\int_a^b{f}=0$, then $f(x)=0$ for all $x\in [a,b]$