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

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

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

domain

- 1 < x < 0 or x > 1

Interval Notation

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

Solution steps

Find non-negative values for radicals:

- 1 \leq x \leq 0 or x \geq 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

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