Question

If $[.]$ denotes the greatest integer function, then the range of $y=\left[e^x(1+\frac{e}{e^x})\right]$ is

• A. $N-\left\{1\right\}$
• B. $[2,\infty )$
• C. $Z$
• D. $R^{+}$

Answer 1

The correct option is A $N-\left\{1\right\}$

Clearly, domain of $y\left(x\right)$ is $R$
$\left[e^x(1+\frac{e}{e^x})\right]=[e^x+e]$
We know that, $e^x>0\forall x\in R$
$\Rightarrow e^x+e>e\approx 2.718\forall x\in R$
$\therefore$ Range is $\{2,3,4,\dots \}$