A log function

Calculus Level pending

If \( f(x)= \ln{x} (x>0),\) which of the following statements is true?

a. There is no \(x\) that satisfies \( \ln{x} = - \frac{1}{x}. \)

b. \( g(x)= {e}^{x}f(x) \) is an increasing function.

c. If \( 0 < a < b ,\) then \(1-\frac{a}{b} < f(\frac{b}{a}) < \frac{b}{a} -1. \)

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