Find all functions satisfying the condition $f(x+y)+f(x)f(y)=f(xy)+f(x)+f(y)$
118727
$g(x+y)+g(x)g(y)=g(xy)+g(x)+g(y)$ for all $x,y$.
156778
Finding functions satisfying $f(f(x))+f(x)+x=0$
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 $
6680
Solve for all possible functions f: $|f(x)-f(y)|=2|x-y|$.
19474
Find all solutions to the functional equation $f(x) +f(x+y)=y+2 $
48592
Prove that $f'$ exists for all $x$ in $R$ if $f(x+y)=f(x)f(y)$ and $f'(0)$ exists
62966
Find all functions $f(x)$ such that $f\left(x^2+f(y)\right)$=$y+(f(x))^2$
31732
If the function $f$ satisfies the equation $f(xf(y)+x)=xy+f(x)$, find $f$
44293
Functions satisfying $f\left( f(x)^2+f(y) \right)=xf(x)+y$
145265
A non-zero function satisfying $g(x+y) = g(x)g(y)$ must be positive everywhere
71049
Functional equation $f(xy)=f(x)+f(y)$ and continuity
109942
Find continuous functions such that $f(x+y)+f(x-y)=2[f(x)+f(y)]$
126931
Find $f(x)$ such that $f(x)+f\left(\frac{1}{x}\right)=f(x)\cdot f\left(\frac{1}{x}\right)$
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 $\mathbb R$
132488
Find all entire functions $f(z)$ such that $|f(z)|=1$ for $|z|=1$
28286
About finding the function such that $f(xy)=f(x)f(y)-f(x+y)+1$
69707
If $f(x + y) \leq yf(x) + f(f(x))$ for all real numbers $x$ and $y$, then prove that $f(x) = 0$ for all $x ≤ 0$.