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Domain

The domain of...

Question

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

A

R

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B

R^{+}

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C

R^{-}

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D

R - {- 1}

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Solution

The correct option is B $R^{+}$
Given $f (x) = \frac{1}{\sqrt{x + | x |}} If x > 0, (x | = x \Rightarrow x + (x | = 2 x which is greater than 0 . If x \leq 0, (x | = - x \Rightarrow x + (x | = 0 f (x) will not be defined if x + (x | = 0 Therefore, the domain of f (x) = R^{+}$

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