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

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

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

domain

f (x) = \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) = 10 x - 4

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

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

\frac{1}{1 + 2 I}

y = \frac{2 x + 1}{x ^{2} - x + 1}

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