AMC 10 2021a Problem 18

Let $f$ be a function defined on the set of positive rational numbers with the property that $f(a\cdot b)=f(a)+f(b)$ for all positive rational numbers $a$ and $b$. Suppose that $f$ also has the property that $f(p)=p$ for every prime number $p$. For which of the following numbers $x$ is $f(x)<0$? $\textbf{(A) }\frac{17}{32} \textbf{(B) }\frac{11}{16} \textbf{(C) }\frac79 \textbf{(D) }\frac76 \textbf{(E) }\frac{25}{11}$