# Crazy Calculus 5

Calculus Level pending

$\large f\left( \dfrac xy \right) = f( x) - f( y)$

Let $$f(x)$$ be defined for all real $$x > 1$$ such that it satisfies the above functional equation for all real $$x$$ and $$y$$ and that $$f(e) =1$$. Which is of the following options is correct?

• $$P: f \left( x \right)$$ is bounded
• $$Q: f\left( \dfrac 1x \right) \to 0$$ as $$x\to 0$$
• $$R: xf\left( x \right) \to 1$$ as $$x \to 0$$
• $$S: f\left( x \right) =\ln x$$
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