Question 135
Let $Q^+$ be the set of all positive rational numbers. Find all functions $f : Q^+ \to Q^+$ satisfying $f(1) = 1$ and
$$
f(x+n) = f(x) + n f\left(\frac{1}{x}\right)
$$
for all positive integers $n$ and all $x \in Q^+$.
$$
f(x+n) = f(x) + n f\left(\frac{1}{x}\right)
$$
for all positive integers $n$ and all $x \in Q^+$.