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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

Options

  1. A(0, 1 e )
  2. B( 1 e , 1 )
  3. C( 1 e , )
  4. D(0,1)

Correct answer

A. (0, 1 e )

Step-by-step solution

For two distinct roots 1+ k 0) k < -1 k < 1 e Hence, k (0, 1 e )

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