Let for all $x > 0$, $f(x) = \lim_{n \rightarrow \infty} n(x^{1/n} - 1)$, then
- A$f(x) + f(\frac{1}{x}) = 1$
- B$f(xy) = f(x) + f(y)$
- C$f(xy) = xf(y) + yf(x)$
- D$f(xy) = xf(x) + yf(y)$
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