Let the sets A and B denote the domain and ra | vedclass

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Question

$f(x)=\frac{1}{\sqrt{\lceil xceil-x}}$

If $x \in I \lceil x ceil=[ x ]$ (greatest integer function)

If $x 
otin I \lceil x ceil=[ x ]+1$

Vedclass · Accepted Answer

only $(S1)$ is true

Vedclass · Answer

$f(x)=\frac{1}{\sqrt{\lceil xceil-x}}$

If $x \in I \lceil x ceil=[ x ]$ (greatest integer function)

If $x 
otin I \lceil x ceil=[ x ]+1$

$\Rightarrow f(x)=\left\{\begin{array}{l}\frac{1}{\sqrt{[x]-x}}, x \in I \frac{1}{\sqrt{[x]+1-x}}, x 
otin I\end{array}ight.$

$\begin{aligned} & \Rightarrow f(x)=\left\{\begin{array}{l}\frac{1}{\sqrt{-\{x\}}}, x \in I, 	ext { (does not exist) } \ \frac{1}{\sqrt{1-\{x\}}}, x 
otin I\end{array}ight. \ & \Rightarrow 	ext { domain of } f(x)=R-I\end{aligned}$

$	ext { Now, } f(x)=\frac{1}{\sqrt{1-\{x\}}}, x 
otin I$

$\Rightarrow 0 < \{x\} < 1$

$\Rightarrow 0 < \sqrt{1-\{x\}} < 1$

$\Rightarrow \frac{1}{\sqrt{1-\{x\}}} > 1$

$\Rightarrow 	ext { Range }(1, \infty)$

$\Rightarrow A=R-I$

$B=(1, \infty)$

$	ext { So, } A \cap B=(1, \infty)-N$

$A \cup B 
eq(1, \infty)$

$\Rightarrow S 1 	ext { is only correct }$

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