Question

Range of the function $f\left(x\right)=\sqrt{\left[x\right]-x}$, where [.] denotes the greatest integer function is

• A. $R$
• B. $\left\{1\right\}$
• C. $\left\{0\right\}$
• D. $(0,\infty )$

Answer 1

The correct option is C $\left\{0\right\}$

$f\left(x\right)=\sqrt{\left[x\right]-x}$
$\left[x\right]-x=0$ (only when x is an integer)
$\left[x\right]-x>0$ (that is not possible)
Range of $f\left(x\right)$ is $\left\{0\right\}$