The domain of the function f ( x ) = 1 [ x ] - 1 , where [ x ] is greatest integer function of x is

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

Domain $=R-\left\{\text{points at which} f\left(x\right)\text{ is not defined}\right\}$

Now, $f\left(x\right)$ will be undefined, when $\left[x\right]-1=0\Rightarrow \left[x\right]=1$

Now, all the values for which the greatest integer function is $1$.

$\Rightarrow x\in [1, 2)$

Therefore, Domain of $f\left(x\right)$ is $R-[1, 2)$