query: Find all functions $f: \mathbb{R} \rightarrow \mathbb {R}$ such that
positive_passages.docid: 111556
positive_passages.text: Solving functional equation $f(x+y)+f(x-y)=2f(x)\cos y$?
negative_passages.docid: 82597
negative_passages.text: How to find $ f(x)$ if $f(1-f(x))=x$ for all $x$ $\in \mathbb{R}$
negative_passages.docid: 20199
negative_passages.text: Find a surjective function $f:\mathbb{N}\to \mathbb{Q}$
negative_passages.docid: 24810
negative_passages.text: Functions satisfying $(b-a)f'(\tfrac{a+b}{2}) = f(b)- f(a)$
negative_passages.docid: 44293
negative_passages.text: Functions satisfying $f\left( f(x)^2+f(y) \right)=xf(x)+y$
negative_passages.docid: 57021
negative_passages.text: Is the set of all functions $f:Z_+\rightarrow Z_+$ that are eventually constant countable.
negative_passages.docid: 108115
negative_passages.text: If $f: [0,1]\rightarrow \mathbb{R}$ is continuous function positive
negative_passages.docid: 28620
negative_passages.text: Function $f(z)$ such that $|f(z)| > |z|$ for every $z\in\mathbb{C}, 1/f(z)$
negative_passages.docid: 65753
negative_passages.text: The Function $f:\mathbb{R}^{2}\rightarrow \mathbb{R}^{2}$ defined by $f(r,\theta)=(r\cos\theta,r\sin\theta)$
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: 95970
negative_passages.text: Let $f:[0,1] \rightarrow \mathbb{R}$ be a continuous function. If $f(0)=f(1)$ then exists $x\in [0,1]$ s.t. $f(x) = f(x+\frac{1}{2})$
negative_passages.docid: 110704
negative_passages.text: Find all functions $f$ such that $f(x)+f(\frac{1}{1-x})=x$
negative_passages.docid: 106853
negative_passages.text: Find all functions: $\left ( \int \frac{dx}{f(x)} \right )\left ( \int f(x)dx \right )=c$
negative_passages.docid: 17700
negative_passages.text: Find all possible functions, $F(r)$, harmonic in $2$ and $3$ dimensions,
negative_passages.docid: 33330
negative_passages.text: Continuous Functions from $\mathbb{R}$ to $\mathbb{Q}$
negative_passages.docid: 29403
negative_passages.text: Finding functions $f: \Bbb R_*^+ \to \Bbb R_*^+$ with certain properties
negative_passages.docid: 104278
negative_passages.text: Finding function $f(x)$ which satisfy given functional equation