query: Find all real functions $f:\mathbb {R} \to \mathbb {R}$ satisfying the equation $f(x^2+y.f(x))=x.f(x+y)$
positive_passages.docid: 17175
positive_passages.text: Problem in solving functional equation $f(x^2 + yf(x)) = xf(x+y)$
negative_passages.docid: 4178
negative_passages.text: Solve $f(x)f(2x^2) = f(2x^3+x)$
negative_passages.docid: 131586
negative_passages.text: Hard functional equation: $ f \big ( x y + f ( x ) \big) = f \big( f ( x ) f ( y ) \big) + x $
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: 103934
negative_passages.text: Functional Equation (no. of solutions): $f(x+y) + f(x-y) = 2f(x) + 2f(y)$
negative_passages.docid: 29647
negative_passages.text: Do there exist functions satisfying $f(x+y)=f(x)+f(y)$ that aren't linear?
negative_passages.docid: 72769
negative_passages.text: How find this function $xf(x^2)=f(x),x>0$
negative_passages.docid: 89257
negative_passages.text: Give an example of a function $f:\mathbb{R}^2 \mapsto \mathbb{R}^2$ such that
negative_passages.docid: 34077
negative_passages.text: Let $f:\mathbb{R}\to\mathbb{R}$ satisfy $f\big(x-f(y)\big)=f\big(f(y)\big)+x\cdot f(y)+f(x)-1$ for all $x,y\in\mathbb{R}$.
negative_passages.docid: 31698
negative_passages.text: $f(m^2 + f(n)) = f(m)^2 + n$ for all natural numbers
negative_passages.docid: 50833
negative_passages.text: Find all $f:\mathbb R\to\mathbb R$ such that $\forall x,y\in\mathbb R$ the given equality holds: $xf(y)+yf(x)=(x+y)f(x)f(y)$.
negative_passages.docid: 66772
negative_passages.text: $f(f(x)f(y))+f(x+y)=f(xy)$
negative_passages.docid: 73519
negative_passages.text: Determine all functions satisfying $f(x + f(x + y)) + f(xy) = x + f(x + y) +yf(x)$
negative_passages.docid: 151519
negative_passages.text: If $f(f(x))=x^2-x+1$, what is $f(0)$?
negative_passages.docid: 50111
negative_passages.text: non-continuous function satisfies $f(x+y)=f(x)+f(y)$
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: 153942
negative_passages.text: Solution of functional equation $f(x+y)=f(x)+f(y)+y\sqrt{f(x)}$