query: Find all solutions to the equation functional $f(x)+f(x+y)=y+2$
positive_passages.docid: 19474
positive_passages.text: Find all solutions to the functional equation $f(x) +f(x+y)=y+2 $
negative_passages.docid: 146719
negative_passages.text: Functional equation $f(r \cos \varphi)+f(r \sin \varphi)=f(r)$
negative_passages.docid: 11806
negative_passages.text: Functional equation.
negative_passages.docid: 88333
negative_passages.text: Find all integral solutions of $y^2=x^3+7$
negative_passages.docid: 76679
negative_passages.text: Prove there are no other solutions of functional equation $f(x+y) = \frac{f(x)+f(y)}{1-f(x)f(y)}$
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: 34074
negative_passages.text: Nonlinear Functional Equation $f(x)^{2}=f\left(\frac x a\right)$
negative_passages.docid: 24862
negative_passages.text: Solving (quadratic) equations of iterated functions, such as $f(f(x))=f(x)+x$
negative_passages.docid: 98255
negative_passages.text: Find $f(x)$ such that $f(f(x)) = x^2 - 2$
negative_passages.docid: 48925
negative_passages.text: BMO1 2009/10 Q5 functional equation: $f(x)f(y) = f(x + y) + xy$
negative_passages.docid: 156778
negative_passages.text: Finding functions satisfying $f(f(x))+f(x)+x=0$
negative_passages.docid: 111556
negative_passages.text: Solving functional equation $f(x+y)+f(x-y)=2f(x)\cos y$?
negative_passages.docid: 13042
negative_passages.text: Finding a function from the given functional equation .
negative_passages.docid: 111467
negative_passages.text: find all natural solution that satisfy $x^2+y^2 = 3z^2$
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: 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: 122329
negative_passages.text: Determine all functions $f(x)$ such that $f(f(x+y))=f(x)+f(y)$