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  4. Domain of the function f(x)=(1/√[x]2-[x]-6) where [x] is greatest integer ≤ x is

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Q. Domain of the function $f(x)=\frac{1}{\sqrt{[x]^{2}-[x]-6}}$ where $[x]$ is greatest integer $\leq x$ is

KCETKCET 2021Relations and Functions

Solution:

$\left[x^{2}\right]-[x]-6>0 ([x]-3)([x]+2)>0$
$[x]<-2,[x]>3$
$\Rightarrow x \in(-\infty,-2) \cup[4, \infty)$