Question

Range of $f\left(x\right)=\frac{e^x}{1+\left[x\right]}$, where $x\ge 0$ is

• A. $[0,\infty )$
• B. $[1,\infty )$
• C. $(-\infty ,\infty )$
• D. $(-\infty ,0]$

Answer 1

The correct option is B $[1,\infty )$

We have for $x\ge 0$, $e^x\ge 1$ and $\left[x\right]\ge 0\Rightarrow 1+\left[x\right]\ge 1$.

So it is evident that the minimum value of $f\left(x\right)$ is going to be $1$ and the maximum is $\infty$ as the function is increasing.

So the range for $f\left(x\right)$ is going to be $[1,\infty )$.