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Given $f (x) = \frac{1}{\sqrt{| x | - x}}$ and $g (x) = \frac{1}{\sqrt{x - | x |}}$ then

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$dom f \neq ϕ$ and dom $g = ϕ$

$dom f = ϕ$ and dom $g \neq ϕ$

$f$ and $g$ have the same domain

$dom f = ϕ and dom g = ϕ$

answer is A.

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Detailed Solution

$dom f = {x : | x | > x}$ and dom $g = {x : x > | x |}$ $= ϕ$ . Thus $dom f = R^{-}$ (the set of all negative real numbers)
and dom $g = ϕ$ .

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