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

The domain of (sqrt(|x|))/(sqrt(|x|)-5) is x 25

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

domain

\frac{∣ x ∣}{∣ x ∣ - 5}

x < - 25 or - 25 < x < 25 or x > 25

Interval Notation

(- \infty, - 25) \cup (- 25, 25) \cup (25, \infty)

Solution steps

Find non-negative values for radicals:

- \infty < x < \infty

Find undefined (singularity) points:

x = - 25, x = 25

Combine real regions and undefined points for final function domain

x < - 25 or - 25 < x < 25 or x > 25

f (x) = \frac{4 + x}{2 - x}

f (x) = \frac{x ^{2}}{6} + 4

\frac{x}{- 4 x + 7}

\frac{6 x ^{2} + 7 x - 3}{3 x ^{2} - 4 x + 1}

f (x) = \frac{1}{5 x - 15}

What is the domain of (sqrt(|x|))/(sqrt(|x|)-5) ?
The domain of (sqrt(|x|))/(sqrt(|x|)-5) is x<-25\lor-25<x<25\lor x>25