Question 44
Determine all continuous functions $f: \mathbb{R}_{+}^{*} \rightarrow \mathbb{R}$ that satisfy the relation
$$
f\left(\frac{x}{y}\right)=\frac{f(x)}{y}-\frac{f(y)}{x}, \quad \forall x, y \in \mathbb{R}_{+}^{*}
$$
$$
f\left(\frac{x}{y}\right)=\frac{f(x)}{y}-\frac{f(y)}{x}, \quad \forall x, y \in \mathbb{R}_{+}^{*}
$$