For $$p, q, r \neq 0$$, let $$f(x) = x^{3} - px^{2} + qx - r, g(x) = x^{3}- \frac{q}{r} x^{2} + \frac{p}{r}x - \frac{1}{r}$$. Which of the following statements is/are true?

I. $$f(a) = 0 \Rightarrow g(\frac{1}{a}) = 0$$
II. $$f(a) = 0 \Rightarrow g(1 + a) = 0$$
III. $$f(a) = 0 \Rightarrow f(\frac{1}{a}) = 0$$

A

All of I, II and II

B

Only II and II

C

Only I and III

D

Only I and II