Question

Find the domain of $f\left(x\right)=\frac{1}{\sqrt{x-\left[x\right]}}$

Answer 1

$f\left(x\right)=\frac{1}{\sqrt{x-\left[x\right]}}$

$x-\left[x\right]>0$

$x>\left[x\right]$

for all $x>0$ and for positive integer $x=\left[x\right]$

$\therefore$ $x$ is defined for all positive numbers except inters $x\in [R^{+}-z]$