The domain of the function f defined by
Question:

The domain of the function $f$ defined by $f(x)=\frac{1}{\sqrt{x-|x|}}$ is

(a) R0

(b) R+

(c) R

(d) none of these

Solution:

$f(x)=f(x)=\frac{1}{\sqrt{x-|x|}}$

f(x) is defined if  − |x| > 0

i.e  x > |x

i.e |x| < x

Since no such real number exist such that |x| < x

$\therefore$ Domain of $f(x)$ is empty set.

Hence, the correct answer is option D.  

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