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The domain of the function $f(x)=\frac{1}{\sqrt{[x]^{2}-3[x]-10}}$ is (where $[x]$ denotes the greatest integer less than or equal to $\mathrm{x}$ )
Option: 1
$(-\infty,-3] \cup[6, \infty)$

Option: 2
$(-\infty,-2) \cup(5, \infty)$

Option: 3
$(-\infty,-3] \cup(5, \infty)$

Option: 4
$(-\infty,-2) \cup[6, \infty)$

Answers (1)

best_answer

$F(x)=\frac{1}{\sqrt{[x]^{2}-3[x]-10}}$
${[\mathrm{x}]^{2}-3[\mathrm{x}]-10>0}$
$([\mathrm{x}]+2)([\mathrm{x}]-5)>0$

$[\mathrm{x}]<-2$ or $[\mathrm{x}]>5$
$[\mathrm{x}] \leq-3$ or $[\mathrm{x}] \geq 6$
$x<-2$ or $x \geq 6$
$\mathrm{x} \in(-\infty,-2) \cup[6, \infty)$

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Ritika Kankaria

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