Question 25
Find all functions $f:\mathbb R_{\gt 0}\to\mathbb R_{\gt 0}$ such that
$$f\left(\frac y{f(x+1)}\right)+f\left(\frac{x+1}{xf(y)}\right)=f(y)$$
for every $x,y\gt 0$.
$$f\left(\frac y{f(x+1)}\right)+f\left(\frac{x+1}{xf(y)}\right)=f(y)$$
for every $x,y\gt 0$.