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

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

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

domain

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

- 1 < x < 0 or x > 1

Interval Notation

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

Solution steps

Find non-negative values for radicals:

- 1 < x < 0 or x > 1

Find undefined (singularity) points:

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

Combine real regions and undefined points for final function domain

- 1 < x < 0 or x > 1

f (x) = \frac{x ^{2} + x - 6}{x ^{2} + 6 x + 9}

f (x) = \frac{x ^{2} - 4 x}{x ^{2} - 16} x = 3.9

2 x - 4

f (x) = x^{2} - 2 x - 15

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