query: Find all functions $f:\mathbb R\to\mathbb R$ such that $f\left(x^2+f(y)\right)=y+f(x)^2$.
positive_passages.docid: 62966
positive_passages.text: Find all functions $f(x)$ such that $f\left(x^2+f(y)\right)$=$y+(f(x))^2$
negative_passages.docid: 141938
negative_passages.text: Find all continuous functions from positive reals to positive reals such that $f(x)^2=f(x^2)$
negative_passages.docid: 19916
negative_passages.text: $f(x)=f(x^2+ 1/4)$ , $f$ is continuous from $\mathbb{R}$ to $\mathbb{R}$
negative_passages.docid: 25953
negative_passages.text: Solving a functional relation $f\left( x \cdot f(y)\right)=x^2 \cdot y^a$
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: 28286
negative_passages.text: About finding the function such that $f(xy)=f(x)f(y)-f(x+y)+1$
negative_passages.docid: 39090
negative_passages.text: Finding functions such that $f(g(x)) = f(x)g(x)$
negative_passages.docid: 75448
negative_passages.text: Find all function satisfying $f(f(n))+f(n)=2n+3k$
negative_passages.docid: 49211
negative_passages.text: Solving $f(x+y) = f(x)f(y)f(xy)$
negative_passages.docid: 13572
negative_passages.text: $x^y+y^x>1$ for all $(x, y)\in \mathbb{R_+^2}$
negative_passages.docid: 129599
negative_passages.text: Functional Equation: Find all functions $f: \mathbb{R} \rightarrow \mathbb{R}$ such that $(x+y)(f(x)-f(y))=(x-y)f(x+y)$
negative_passages.docid: 50012
negative_passages.text: $f: [a,b] \to \mathbb{R}$, $f(a) = f(b)$. Show $\exists c \in [a, \frac{a+b}{2} ]$ with $f(c)=f(c+\frac{b-a}{2})$
negative_passages.docid: 153942
negative_passages.text: Solution of functional equation $f(x+y)=f(x)+f(y)+y\sqrt{f(x)}$
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: 155165
negative_passages.text: Prove that $\mathbb F_8=\mathbb F_2[X]/(X^3+X+1)$
negative_passages.docid: 106748
negative_passages.text: Number of functions $f : A \to A$ such that $f(f(x))=f(x)$
negative_passages.docid: 409
negative_passages.text: functions satisfying $f(x - y) = f(x) f(y) - f(a - x) f(a + y)$ and $f(0)=1$