Question

The number of real solutions of the equation $e^x+x=0$

• A. $0$
• B. $2$
• C. $1$
• D. None of these

Answer 1

Answer: (C)

$1$

Let $f\left(x\right)=x+e^x\Rightarrow f^{\prime }\left(x\right)=1+e^x>0,\forall x\in R$
Thus f is strictly increasing function for all $x$
Also $\underset{x\to -\infty }{lim}f\left(x\right)=-\infty$ and ${lim}_{x\to \infty }f\left(x\right)=\infty$
Hence $f$ has exactly one real solution.