Question 14
Find all functions $f: \mathbb{R} \rightarrow \mathbb{R}$ which satisfy
$$
\begin{aligned}
& f\left(\frac{\sqrt{3}}{3} x\right)=\sqrt{3} f(x)-\frac{2 \sqrt{3}}{3} x \\
& f(x) f(y)=f(x y)+f\left(\frac{x}{y}\right)
\end{aligned}
$$
for all $x, y \in \mathbb{R}$, with $y \neq 0$.
$$
\begin{aligned}
& f\left(\frac{\sqrt{3}}{3} x\right)=\sqrt{3} f(x)-\frac{2 \sqrt{3}}{3} x \\
& f(x) f(y)=f(x y)+f\left(\frac{x}{y}\right)
\end{aligned}
$$
for all $x, y \in \mathbb{R}$, with $y \neq 0$.