Let
![\mathbb{R} ^{+}](/media/m/c/b/c/cbc0e2cb919e248673ab4a6f5c4212f4.png)
denote the set of all positive real numbers. Find all functions
![\mathbb{R} ^{+} \to \mathbb{R} ^{+}](/media/m/c/4/a/c4a180b89ac05953d40bc121274ecfe2.png)
such that
![f(x+f(y)) = yf(xy+1)](/media/m/0/2/3/0230142bc0f665741f5f34c3e2335386.png)
holds for all
![x, y \in \mathbb{R} ^{+}](/media/m/a/6/c/a6c811fd818b182b23cedfc5b54ac08d.png)
.
%V0
Let $\mathbb{R} ^{+}$ denote the set of all positive real numbers. Find all functions $\mathbb{R} ^{+} \to \mathbb{R} ^{+}$ such that
$$f(x+f(y)) = yf(xy+1)$$
holds for all $x, y \in \mathbb{R} ^{+}$.