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

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

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

domain

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

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

Interval Notation

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

Solution steps

Find non-negative values for radicals:

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

Find undefined (singularity) points:

x = 0

Combine real regions and undefined points for final function domain

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

f (x) = (x^{2} + 1) - 1

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

f (x) = x e^{- x^{2}}

f (x) = x + 2 + \frac{1}{x - 3}

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

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