What is the domain of f(x)= 1/(sqrt(|x^3-x|)) ?

The domain of f(x)= 1/(sqrt(|x^3-x|)) is x 1

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domain of f(x)= 1/(sqrt(|x^3-x|))

domain

f (x) = \frac{1}{∣ x ^{3} - x ∣}

x < - 1 or - 1 < x < 0 or 0 < x < 1 or x > 1

Interval Notation

(- \infty, - 1) \cup (- 1, 0) \cup (0, 1) \cup (1, \infty)

Solution steps

Find non-negative values for radicals:

- \infty < x < \infty

Find undefined (singularity) points:

x = - 1, x = 0, x = 1

Combine real regions and undefined points for final function domain

x < - 1 or - 1 < x < 0 or 0 < x < 1 or x > 1

f (x) = \frac{1}{8 x - 24}

2 sin (\frac{π}{2} x + 2) - 3

25 (\frac{1}{5})^{x - 2} - 1

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

f (x) = \frac{1}{x + 19}

What is the domain of f(x)= 1/(sqrt(|x^3-x|)) ?
The domain of f(x)= 1/(sqrt(|x^3-x|)) is x<-1\lor-1<x<0\lor 0<x<1\lor x>1