Find all functions $f:\mathbb{R}\to\mathbb{R}$ for which 
\[ x(f(x+1)-f(x)) = f(x), \] 
for all $x\in\mathbb{R}$ and 
\[ | f(x) - f(y) | \leq |x-y| , \] 
for all $x,y\in\mathbb{R}$. 

[i]Mihai Piticari[/i]