What is the domain of f(x)=sqrt((x^2-6)/(x^2-1)) ?

The domain of f(x)=sqrt((x^2-6)/(x^2-1)) is x = sqrt(6)

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domain of f(x)=sqrt((x^2-6)/(x^2-1))

domain

x \leq - 6 or - 1 < x < 1 or x \geq 6

Interval Notation

(- \infty, - 6] \cup (- 1, 1) \cup [6, \infty)

Solution steps

Find non-negative values for radicals:

x \leq - 6 or - 1 < x < 1 or x \geq 6

Find undefined (singularity) points:

x = 1, x = - 1

Combine real regions and undefined points for final function domain

x \leq - 6 or - 1 < x < 1 or x \geq 6

What is the domain of f(x)=sqrt((x^2-6)/(x^2-1)) ?
The domain of f(x)=sqrt((x^2-6)/(x^2-1)) is x<=-sqrt(6)\lor-1<x<1\lor x>= sqrt(6)