Question 134
Let $\mathbb{R}_{+}^{*}$ be the set of strictly positive reals. Find all functions $f: \mathbb{R}_{+}^{*} \longrightarrow \mathbb{R}_{+}^{*}$ such as for all $x, y\gt 0$, ON AIT $$
f\left(\frac{f(x)}{y f(x)+1}\right)=\frac{x}{x f(y)+1}
$$
f\left(\frac{f(x)}{y f(x)+1}\right)=\frac{x}{x f(y)+1}
$$