Question

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

• A. R
• B. R-Z
• C. Z
• D. None of these

Answer 1

Answer: (B)

R-Z

The function is defined as

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

The function is not defined if

$\sqrt{x-\left[x\right]}=0$

$⟹x-\left[x\right]=0$

$⟹x=\left[x\right]$

This happens only in the case of Integers

So The function is not defined at Integer Values

Hence , The Domain of function is $R-Z$