query: Solving the functional Equation $f(f(x))=f(x)+x$
positive_passages.docid: 24862
positive_passages.text: Solving (quadratic) equations of iterated functions, such as $f(f(x))=f(x)+x$
negative_passages.docid: 76458
negative_passages.text: Solve the following functional equation $f(xf(y))+f(yf(x))=2xy$
negative_passages.docid: 53024
negative_passages.text: $f(x)f(1/x)=f(x)+f(1/x)$
negative_passages.docid: 34074
negative_passages.text: Nonlinear Functional Equation $f(x)^{2}=f\left(\frac x a\right)$
negative_passages.docid: 47212
negative_passages.text: Solving functional equation
negative_passages.docid: 37976
negative_passages.text: Find all functions $f$ such that $(x+y)f(x)+f(y^2)=(x+y)f(y)+f(x^2)$
negative_passages.docid: 133333
negative_passages.text: Find $f(x)$ for $f(f(x))=\sin x$
negative_passages.docid: 23485
negative_passages.text: Solving $\forall x \in \mathbb{R}_+^*, f'(x) = f\left(\frac1{x}\right)$
negative_passages.docid: 75448
negative_passages.text: Find all function satisfying $f(f(n))+f(n)=2n+3k$
negative_passages.docid: 48652
negative_passages.text: Solve the functional equation $2f(x)=f(ax)$ for some $a$.
negative_passages.docid: 1071
negative_passages.text: Determine all functions $f:\mathbb{N}\rightarrow\mathbb{N}$ such that $xf(y)+yf(x)=(x+y)f(x^2+y^2)$ for all $x,y\in\mathbb{N}$ (contest question)
negative_passages.docid: 11806
negative_passages.text: Functional equation.
negative_passages.docid: 146719
negative_passages.text: Functional equation $f(r \cos \varphi)+f(r \sin \varphi)=f(r)$
negative_passages.docid: 148227
negative_passages.text: Rewriting of functional equation $f(xy)=f(x)+f(y)$
negative_passages.docid: 136475
negative_passages.text: d'Alembert-like functional equation: $f(x+y)+g(x-y)=\lambda f(x)g(y)$
negative_passages.docid: 104209
negative_passages.text: Functional equation - Cyclic Substitutions
negative_passages.docid: 109942
negative_passages.text: Find continuous functions such that $f(x+y)+f(x-y)=2[f(x)+f(y)]$