Video solution:

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Written solution:

Note that for any number of the form $p^e$ where $p$ is prime, $$f(p^e) = ef(p) = ep.$$ This can be seen by applying the function property multiple times.

Also note that $$\begin{align*}f(a) &= f\left(\dfrac{a}{b} \cdot b\right) \\&= f\left(\dfrac{a}{b}\right) + f(b),\end{align*}$$ which gives us $$f\left(\dfrac{a}{b}\right) = f(a) - f(b).$$

We can now calculate each answer choice one-by-one.

$$f\left(\dfrac{17}{32}\right) = f(17) - f(32)$$ $$= 17 - 5 \cdot 2 = 7.$$

$$\begin{gather*} f\left(\dfrac{11}{16}\right) = f(11) - f(16) \\ = 11 - 4 \cdot 2 = 3 \end{gather*}$$

$$\begin{gather*} f\left(\dfrac{7}{9}\right) = f(7) - f(9) \\ = 7 - 2 \cdot 3 = 1 \end{gather*}$$

$$\begin{gather*} f\left(\dfrac{7}{6}\right) = f(7) - f(6) \\ = 7 - f(2) - f(3) = 2 \end{gather*}$$

$$\begin{gather*} f\left(\dfrac{25}{11}\right) = f(25) - f(11) \\ = 2 \cdot 5 - 11 = -1 \end{gather*}$$

Thus, E is the correct answer.