What is the domain of (sqrt(|x|))/(sqrt(|x|-5)) ?

The domain of (sqrt(|x|))/(sqrt(|x|-5)) is x 5

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domain of (sqrt(|x|))/(sqrt(|x|-5))

domain

\frac{∣ x ∣}{∣ x ∣ - 5}

x < - 5 or x > 5

Interval Notation

(- \infty, - 5) \cup (5, \infty)

Solution steps

Find non-negative values for radicals:

x \leq - 5 or x \geq 5

Find undefined (singularity) points:

x = - 5, x = 5

Combine real regions and undefined points for final function domain

x < - 5 or x > 5

f (x) = 3^{x - 3}

f (x) = \frac{x ^{2}}{9 - x}

f (x) = x^{2} + 86

f (x) = arccos (x^{2})

f (x) = 3 x^{2} - 4

What is the domain of (sqrt(|x|))/(sqrt(|x|-5)) ?
The domain of (sqrt(|x|))/(sqrt(|x|-5)) is x<-5\lor x>5