query: Find all functions that satisfy $f(x+f(y))=f(x)-y$
positive_passages.docid: 11806
positive_passages.text: Functional equation.
negative_passages.docid: 81799
negative_passages.text: Examples of functions where $f(ab)=f(a)+f(b)$
negative_passages.docid: 32599
negative_passages.text: Solution to the functional equation $f(x^y)=f(x)^{f(y)}$
negative_passages.docid: 34223
negative_passages.text: Prove that every function that verifies $|f(x)-f(y)|\leq(x-y)^2$ for all $x,y$ is constant.
negative_passages.docid: 117848
negative_passages.text: Find all entire functions
negative_passages.docid: 49211
negative_passages.text: Solving $f(x+y) = f(x)f(y)f(xy)$
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: 125788
negative_passages.text: A function with a property $f(x+y)=f(x)f(y)$
negative_passages.docid: 126931
negative_passages.text: Find $f(x)$ such that $f(x)+f\left(\frac{1}{x}\right)=f(x)\cdot f\left(\frac{1}{x}\right)$
negative_passages.docid: 86128
negative_passages.text: Find all functions $ f : \Bbb R \to \Bbb R$ which satisfy $f(x)f(y) = f(x + y) + xy$ for all $x, y ∈ \Bbb R$.
negative_passages.docid: 104278
negative_passages.text: Finding function $f(x)$ which satisfy given functional equation
negative_passages.docid: 109942
negative_passages.text: Find continuous functions such that $f(x+y)+f(x-y)=2[f(x)+f(y)]$
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: 20568
negative_passages.text: Does the following have a solution for f(x,y)?
negative_passages.docid: 31732
negative_passages.text: If the function $f$ satisfies the equation $f(xf(y)+x)=xy+f(x)$, find $f$
negative_passages.docid: 50111
negative_passages.text: non-continuous function satisfies $f(x+y)=f(x)+f(y)$
negative_passages.docid: 71049
negative_passages.text: Functional equation $f(xy)=f(x)+f(y)$ and continuity