Find all the functions for which $f(x^{2})-f(y^{2})=(x+y)(f(x)-f(y)):\forall x, y\in\mathbb{R}$
37976
Find all functions $f$ such that $(x+y)f(x)+f(y^2)=(x+y)f(y)+f(x^2)$
29403
Finding functions $f: \Bbb R_*^+ \to \Bbb R_*^+$ with certain properties
26754
Find all continuous functions satisfying $\int_0^xf=(f(x))^2+C$ for some constant $C \neq 0$.
55693
The functional equation $ f \big( x - f ( y ) \big) = f \big( f ( y ) \big) + x f ( y ) + f ( x ) - 1 $
74950
Show a function for which $f(x + y) = f(x) + f(y) $ is continuous at zero if and only if it is continuous on $\mathbb R$
19474
Find all solutions to the functional equation $f(x) +f(x+y)=y+2 $
133333
Find $f(x)$ for $f(f(x))=\sin x$
104278
Finding function $f(x)$ which satisfy given functional equation
49794
Solve $f(x^2+y+f(y))=2y+f(x)^2$ over $\mathbb{R}$
65946
A function $f: \mathbb R \to \mathbb R$ satisfies equation $f(x+y)=f(x)f(y)$ for all $x,y\in \mathbb R $
144473
Finding all functions $ f : \mathbb N^*\to\mathbb N^*$ such that for every $ x , y \in \mathbb N ^ * $, $ f ( x ) + f ( y ) \mid x ^ n + y ^ n $
41226
Find $f:f(xf(x)+f(y))=f(x)^2+y$
29647
Do there exist functions satisfying $f(x+y)=f(x)+f(y)$ that aren't linear?
144222
If $f(x + 1) + f(x − 1) = f(x), \forall x \in \mathbb{R}$,then how to find $k$ such that $f(x + k) = f(x)$?
13248
How to obtain $f(x)$, if it is known that $f(f(x))=x^2+x$?
44670
Find all functions $f: \mathbb Z \to \mathbb Z$ such that $f(x+y)=f(x)+f(y)$
43667
Is $f(x,y(x))$ a function of two variables? If so, how is that possible?