Question

Find the domain of the following functions given by f(x) = `1/sqrt(x + |x|)`

Answer 1

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⁺