What is the domain of 1/(sqrt(x)ln(x^2-1)) ?

The domain of 1/(sqrt(x)ln(x^2-1)) is 1 sqrt(2)

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domain of 1/(sqrt(x)ln(x^2-1))

domain

\frac{1}{x ln ( x ^{2} - 1 )}

1 < x < 2 or x > 2

Interval Notation

(1, 2) \cup (2, \infty)

Solution steps

Find non-negative values for radicals:

x \geq 0

Find positive values for logs:

x < - 1 or x > 1

Find undefined (singularity) points:

x = 2

Combine real regions and undefined points for final function domain

1 < x < 2 or x > 2

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