What is the domain of sqrt((x^3+x)/(x^2-1)) ?

The domain of sqrt((x^3+x)/(x^2-1)) is -1 1

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domain of sqrt((x^3+x)/(x^2-1))

domain

\frac{x ^{3} + x}{x ^{2} - 1}

- 1 < x \leq 0 or x > 1

Interval Notation

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

Solution steps

Find non-negative values for radicals:

- 1 < x \leq 0 or x > 1

Find undefined (singularity) points:

x = 1, x = - 1

Combine real regions and undefined points for final function domain

- 1 < x \leq 0 or x > 1

f (x) = \frac{1 - x}{x ^{2} - 4}

f (x) = 3 + \frac{2}{x}

f (x) = 3 x - 11

f (x) = \frac{x - 1}{x ^{2} + 4 x - 5}

y = \frac{x}{x + 4}

What is the domain of sqrt((x^3+x)/(x^2-1)) ?
The domain of sqrt((x^3+x)/(x^2-1)) is -1<x<= 0\lor x>1