Question

The domain of the function f defined by $f\left(x\right)=\frac{1}{\sqrt{x-\left|x\right|}}$ is
(a) R₀
(b) R⁺
(c) R⁻
(d) none of these

Answer 1

f(x) = $f\left(x\right)=\frac{1}{\sqrt{x-\left|x\right|}}$
f(x) is defined if x − |x| > 0
i.e x > |x|
i.e |x| < x
Since no such real number x exist such that |x| < x
$\therefore$ Domain of f(x) is empty set.
Hence, the correct answer is option D.