Question

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

• A. Z
• B. R
• C. $R-Z^{+}$
• D. $R-Z$

Answer 1

The correct option is D $R-Z$

$f\left(x\right)=\frac{1}{\sqrt{x-\left(x\right]}}\mathrm{If}x\in Z,\left(x\right]=x\Rightarrow x-\left(x\right]=0\therefore f\left(x\right)\mathrm{is}\mathrm{not}\mathrm{defined}\mathrm{if}x\in Z.\mathrm{If}x\in R-Z,0<x-\left(x\right]<1\Rightarrow f\left(x\right)\mathrm{exists}\mathrm{for}\mathrm{all}x\in R-Z.\mathrm{So},\mathrm{the}\mathrm{domain}\mathrm{of}f\left(x\right)\mathrm{is}R-Z.$