Question

The domain of the function $f\left(x\right)={\log }_e(x-[x\left]\right)$ is (where $[.]$ represents the greatest integer function)

• A. $R$
• B. $R-Z$
• C. $(0,\infty )$
• D. $(-\infty ,0)$

Answer 1

The correct option is B $R-Z$

For $\log$ to be defined
$x–\left[x\right]>0$
we know that
$x-\left[x\right]=\left\{x\right\}\in [0,1)$

For the function to be defined $\left\{x\right\}>0$
$\Rightarrow \left\{x\right\}\ne 0\Rightarrow x\notin Z$
$\therefore x\in R-Z$