Mathematics - Functions Question with Solution | TestHub

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