Is $g:R\rightarrow R$ a surjective function if $g(2xy+g(x))+g(g(y)g(x)+x)=g(2xg(y)+g(x))+g(yg(x)+x)$.
The problem was given by my friend but I am unable to make any progress except trying to work on few substitutions such as $y=\frac{(y-1)g(x)}{2x}+1$.