Question 10
Let $\mathbb R_{\gt0}$ denote the set of strictly positive real numbers. Find all functions $f:\mathbb R_{\gt0}\to\mathbb R_{\gt0}$ such that
$$f(x+f(xy))+y=f(x)f(y)+1$$
for all strictly positive real numbers $x,y$.
$$f(x+f(xy))+y=f(x)f(y)+1$$
for all strictly positive real numbers $x,y$.