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Question
Find the domain of the following functions given by f(x) = `1/sqrt(x + |x|)`
Solution
For real value of f
x + |x| > 0
When x > 0,
x + |x| > 0
⇒ x + x > 0
⇒ 2x > 0
⇒ x > 0
When x < 0,
x + |x| > 0
⇒ x – x > 0
⇒ 2x > 0
⇒ x > 0
So, x > 0, to satisfy the given equation.
Therefore, the domain of f = R+
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