query: Find all solutions $f:\mathbb R \to \mathbb R$ to the functional equation $g(f(x+y)) = g(f(x)) + g(f(y))$
positive_passages.docid: 157744
positive_passages.text: Cauchy's functional equation with composite function: $gf(x+y)=gf(x)+gf(y)$
negative_passages.docid: 23186
negative_passages.text: $f: \mathbb{R^2} \to \mathbb{R}$ a $C^\infty$ function such that $f(x,0)=f(0,y)=0$ then exists $g$ such that $f(x,y)=xy\, g(x,y)$
negative_passages.docid: 23485
negative_passages.text: Solving $\forall x \in \mathbb{R}_+^*, f'(x) = f\left(\frac1{x}\right)$
negative_passages.docid: 111789
negative_passages.text: Solving functional differential equation $f'(x)=2f(2x)-f(x)$
negative_passages.docid: 29403
negative_passages.text: Finding functions $f: \Bbb R_*^+ \to \Bbb R_*^+$ with certain properties
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: 103934
negative_passages.text: Functional Equation (no. of solutions): $f(x+y) + f(x-y) = 2f(x) + 2f(y)$
negative_passages.docid: 55286
negative_passages.text: Functional equation: $f: \mathbb{R} \rightarrow \mathbb{R}$, $f((x + 1) f(y)) = y (f(x) + 1)$
negative_passages.docid: 62744
negative_passages.text: Does the functional equation $f(1/r) = rf(r)$ have any nontrivial solutions besides $f(r) = 1/\sqrt{r}$?
negative_passages.docid: 11453
negative_passages.text: Find a real function $f:\mathbb{R}\to\mathbb{R}$ such that $f(f(x)) = -x$?
negative_passages.docid: 44670
negative_passages.text: Find all functions $f: \mathbb Z \to \mathbb Z$ such that $f(x+y)=f(x)+f(y)$
negative_passages.docid: 146719
negative_passages.text: Functional equation $f(r \cos \varphi)+f(r \sin \varphi)=f(r)$
negative_passages.docid: 19019
negative_passages.text: Find all functions $f:\Bbb{Q}\rightarrow \Bbb{Q}$ such that $f(x)+f(t)=f(y)+f(z)$ for all rational numbers $x<y<z<t$ that form an AP
negative_passages.docid: 122329
negative_passages.text: Determine all functions $f(x)$ such that $f(f(x+y))=f(x)+f(y)$
negative_passages.docid: 48652
negative_passages.text: Solve the functional equation $2f(x)=f(ax)$ for some $a$.
negative_passages.docid: 39090
negative_passages.text: Finding functions such that $f(g(x)) = f(x)g(x)$
negative_passages.docid: 81055
negative_passages.text: Functional Equation simple problem