Find all $f$ such that $f(xy+f(x))=f(f(x)f(y))+x, \forall x,y\in \mathbb{R}_{>0}$
131586
Hard functional equation: $ f \big ( x y + f ( x ) \big) = f \big( f ( x ) f ( y ) \big) + x $
104278
Finding function $f(x)$ which satisfy given functional equation
11453
Find a real function $f:\mathbb{R}\to\mathbb{R}$ such that $f(f(x)) = -x$?
71049
Functional equation $f(xy)=f(x)+f(y)$ and continuity
132488
Find all entire functions $f(z)$ such that $|f(z)|=1$ for $|z|=1$
82597
How to find $ f(x)$ if $f(1-f(x))=x$ for all $x$ $\in \mathbb{R}$
48592
Prove that $f'$ exists for all $x$ in $R$ if $f(x+y)=f(x)f(y)$ and $f'(0)$ exists
28007
Assuming: $\forall x \in [0,1]:f(x) > x$ Prove: $\forall x \in [0,1]:f(x) > x + \varepsilon $
50012
$f: [a,b] \to \mathbb{R}$, $f(a) = f(b)$. Show $\exists c \in [a, \frac{a+b}{2} ]$ with $f(c)=f(c+\frac{b-a}{2})$
29647
Do there exist functions satisfying $f(x+y)=f(x)+f(y)$ that aren't linear?
53024
$f(x)f(1/x)=f(x)+f(1/x)$
17119
Find all strictly monotone $f:(0,+\infty) \to (0, +\infty)$ such that $f(\frac{x^2}{f(x)})=x.$
14495
I need to find all functions $f:\mathbb R \rightarrow \mathbb R$ which are continuous and satisfy $f(x+y)=f(x)+f(y)$
144222
If $f(x + 1) + f(x − 1) = f(x), \forall x \in \mathbb{R}$,then how to find $k$ such that $f(x + k) = f(x)$?
13202
Prove that there exists at least one $x_0\in\mathbb{R}$, such that $f(x_0)+f''(x_0)=0$
66772
$f(f(x)f(y))+f(x+y)=f(xy)$
122329
Determine all functions $f(x)$ such that $f(f(x+y))=f(x)+f(y)$