Question

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

• A. f(x) is bounded
• B. $f \left( \frac{1}{x} \right) \to 0$ as $x \to 0 $
• C. $x f(x) \to 1$ as $x \to 0$
• D. f(x) = ln x

Answer 1

Answer: (D)

Correct answer is (d) f(x) = ln x