Algebra Level 3

Let the function \(f\) be defined by \(f(x) = ke^x + x\), where \(k\) is a real number independent of \(x\).

The intermediate value theorem shows that this function has at least one root in the interval \(]0,1[\).

Which one of the following intervals can \(k\) belong?

\[ \] \[ \] \[ \]

Clarification: \(e\) denotes Euler's number, \(e \approx 2.71828\).


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