Question 71
Let $\mathbb{Q}^{+}$ be the set of positive rational numbers. Find all functions $f: \mathbb{Q}^{+} \rightarrow \mathbb{R}$ such that $f(1)=1$, $f(1 / x)=f(x)$ for any $x \in \mathbb{Q}^{+}$ and $x f(x)=(x+1) f(x-1)$ for any $x \in \mathbb{Q}^{+}, x\gt 1$.