The domain of the function $f(x)=\frac{1}{\sqrt{[x]^{2}-3[x]-10}}$ is : ( where $[\mathrm{x}]$ denotes the greatest integer less than or equal to $x$ )
Solution
$f(x)=\frac{1}{\sqrt{[x]^2-3[x]-10}}$
<br/><br/>For Domain $[x]^2-3[x]-10>0$
<br/><br/>$$
\begin{aligned}
& \Rightarrow ([x]-5)([x]+2)>0 \\\\
& \Rightarrow [x] \in(-\infty,-2) \cup(5, \infty) \\\\
& \therefore x \in(-\infty,-2) \cup[6, \infty)
\end{aligned}
$$
About this question
Subject: Mathematics · Chapter: Sets, Relations and Functions · Topic: Sets and Operations
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