Question 40
Let $Q^+$ denote the set of positive rational numbers. Determine all functions $f: Q^+ \to Q^+$ that satisfy the conditions
$$
f\left(\frac{x}{x+1}\right) = \frac{f(x)}{x+1} \quad \text{and} \quad f\left(\frac{1}{x}\right) = \frac{f(x)}{x^3}
$$
for all $x \in Q^+$.
$$
f\left(\frac{x}{x+1}\right) = \frac{f(x)}{x+1} \quad \text{and} \quad f\left(\frac{1}{x}\right) = \frac{f(x)}{x^3}
$$
for all $x \in Q^+$.