Question

Find the domain of the following function:

$f\left(x\right)=\log (x-[x\left]\right),$ where $[\cdot ]$ denotes the greatest integer function

Answer 1

Given function is, $f\left(x\right)=\log (x-[x\left]\right)$
For this function to be defined, $x-\left[x\right]>0$
We know $\left[x\right]<x$ except for integral values of $x$ and $x=\left[x\right]$ for integral values
Hence Domain of the given function is, $x\in R-I$