Question

Find the range of $y=\frac{e^{-x}}{1+\left[x\right]}$

• A. $(-\infty ,\infty )$
• B. $R-0$
• C. $R$
• D. None of these

Answer 1

The correct option is B $R-0$

We have, $y=\frac{e^{-x}}{1+\left[x\right]}$

$\Rightarrow (1+\left[x\right])y=e^{-x}>0$

$\Rightarrow (1+\left[x\right])y>0$
$\Rightarrow y>0$ if $1+\left[x\right]>0$

and $y<0$ if $1+\left[x\right]<0$
$\therefore y\in R-\left\{0\right\}$