Paragraph: If a continuous $f$ defined on the real line $R$, assume positive and negative values in $R$, then the equation $f(x)=0$ has a root in $R$. For example, if it is known that a continuous function $f$ on $R$ is positive at some point and its minimum values is negative, then the equation $f(x)=0$ has a root in $R$. Consider $f(x)=k e^x-x$ for all real $x$, where $k$ is real constant.Question: For $k>0$, the set of all values of $k$ for which $k e^x-x=0$ has two distinct roots, is

• Correct answer
  A

  $\left(0, \frac{1}{e}\right)$
• B

  $\left(\frac{1}{e}, 1\right)$
• C

  $\left(\frac{1}{e}, \infty\right)$
• D

  $(0,1)$

Hence, the correct answer is option: 'A'.