Let f (x) be defined for all x > 0 and be continuous. Let f (x) satisfy $\mathrm{f}\left(\frac{\mathrm{x}}{\mathrm{y}}\right)=\mathrm{f}\left(\mathrm{x}\right)-\mathrm{f}\left(\mathrm{y}\right)$ for all x, y and f (e) = 1. Then

• A

  f (x) is bounded

• B

  $\mathrm{f}\left(\frac{1}{\mathrm{x}}\right)\to 0\text{ as }\mathrm{x}\to 0$

• C

  x f (x) → 0 as x → 0

• D

  f (x) = log x