Question

The range of the function $f\left(x\right)=e^x-e^{-x}$, is

• A. $[0,\infty )$
• B. $(-\infty ,0)$
• C. $(-\infty ,\infty )$
• D. None

Answer 1

The correct option is C $(-\infty ,\infty )$

Given, $f\left(x\right)=e^x-e^{-x}$
$\therefore f^{\prime }\left(x\right)=e^x+e^{-x}>0\forall x\in R$
Thus $f\left(x\right)$ is strictly increasing function and it is continuous as well,
Now $f(-\infty )=-\infty$ and $f\left(\infty \right)=\infty$
Hence range of $f\left(x\right)$ is $(-\infty ,\infty )$