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

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

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

domain

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

x < - 1 or 0 \leq x < 1

Interval Notation

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

Solution steps

Find non-negative values for radicals:

x < - 1 or 0 \leq x < 1

Find undefined (singularity) points:

x = 1, x = - 1

Combine real regions and undefined points for final function domain

x < - 1 or 0 \leq x < 1

f (x) = \frac{x - 3}{x ^{2} - 9}

f (x) = \frac{2 x ^{2} + 5}{x ^{2} - 25}

\frac{7}{x ^{2} - 14 x - 32}

f (x) = 3 (2^{x})

f (x) = 15 cos (3 x - \frac{3 π}{5}) - 7

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