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

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

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

domain

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

- 1 \leq x < 0 or x \geq 1

Interval Notation

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

Solution steps

Find non-negative values for radicals:

- 1 \leq x < 0 or x \geq 1

Find undefined (singularity) points:

x = 0

Combine real regions and undefined points for final function domain

- 1 \leq x < 0 or x \geq 1

f (x) = ln (x^{2} - 5)

f (x) = e^{- x} + 4

f (x) = \frac{3 e ^{x}}{e ^{x} - 2}

f (x) = 2 sin (2 x)

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