Question

The domain of the function $f\left(x\right)=\sqrt{\left[x\right]-1}$ is, (where [ ] represent the greatest integer function)

Answer 1

$f\left(x\right)=\sqrt{\left[x\right]-1}$
$\left[x\right]-1>0$ ($\because$ quantity inside square root should be positive)
$\therefore \left[x\right]>1$
$\therefore xϵ(1,\infty )$
$\therefore$Domain$=(1,\infty )$