What is the domain of f(x)=sqrt((x^2-4)/(x-x^3)) ?

The domain of f(x)=sqrt((x^2-4)/(x-x^3)) is x<=-2\lor-1<x<0\lor 1<x<= 2

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domain of f(x)=sqrt((x^2-4)/(x-x^3))

domain

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

x \leq - 2 or - 1 < x < 0 or 1 < x \leq 2

Interval Notation

(- \infty, - 2] \cup (- 1, 0) \cup (1, 2]

Solution steps

Find non-negative values for radicals:

x \leq - 2 or - 1 < x < 0 or 1 < x \leq 2

Find undefined (singularity) points:

x = 0, x = - 1, x = 1

Combine real regions and undefined points for final function domain

x \leq - 2 or - 1 < x < 0 or 1 < x \leq 2

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

f (x) = \frac{14 x}{x ^{2} + 49}

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

(- 1, 3), (8, - 5)

- 8 x^{2} + 4 x - 2

What is the domain of f(x)=sqrt((x^2-4)/(x-x^3)) ?
The domain of f(x)=sqrt((x^2-4)/(x-x^3)) is x<=-2\lor-1<x<0\lor 1<x<= 2