Question

The domain of the function $f\left(x\right)=3-\frac{1}{[x+3]}$ is
(where [.] denotes the greatest integer function)

Answer 1

$f\left(x\right)=3-\frac{1}{[x+3]}$
For function to be defined,
$[x+3]\ne 0\Rightarrow \left[x\right]+3\ne 0(\because [x+Z]=[x]+Z)\Rightarrow \left[x\right]\ne -3\Rightarrow x\notin [-3,-2)$
$\therefore$ Domain of $f\left(x\right)=R-[-3,-2)$