Question 24
Find all functions $f: \mathbb{R}^{+} \rightarrow \mathbb{R}^{+}$ such that
$$
(z+1) f(x+y) = f(x f(z) + y) + f(y f(z) + x)
$$
for all positive real numbers $x$, $y$, $z$.
$$
(z+1) f(x+y) = f(x f(z) + y) + f(y f(z) + x)
$$
for all positive real numbers $x$, $y$, $z$.