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

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

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

domain

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

x < - 1 or 0 \leq x < 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) = lo g_{12} (∣ 15 - 24 x ∣)

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

5 x + 2

\frac{5 x}{14 - x}

f (x) = (x^{2} - 4)^{\frac{5}{3}}

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