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Model Paper 1 — MATHS STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 ScienceMATHSModel Paper 12 Marks
Question
Write the domain of the real function $f(x)=\frac{1}{\sqrt{|x|-x}}$
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Answer

Case I : When x > 0.Then,we have, 
$\begin{array}{l}|x|= x \\ 
\Rightarrow \frac{1}{\sqrt{|x|-x}}=\frac{1}{\sqrt{x-x}}=\frac{1}{0}=\infty\end{array}$
Case II : When x < 0 
$\begin{array}{l}| x |=- x \\ \Rightarrow \frac{1}{\sqrt{|x|-x}}=\frac{1}{\sqrt{-x-x}}=\frac{1}{\sqrt{-2 x}}(\text { exists because when } x <0,-2 x >0)\end{array}$
$\Rightarrow f ( x )$ is defined when $x <0$
Therefore, domain $=(-\infty, 0)$

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