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

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

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

domain

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

- 2 < x < - 1 or x > 2

Interval Notation

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

Solution steps

Find non-negative values for radicals:

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

Find undefined (singularity) points:

x = 2, x = - 2

Combine real regions and undefined points for final function domain

- 2 < x < - 1 or x > 2

f (y) = \frac{4 - y ^{2}}{1}

f (x) = - e - x + 4

\frac{3}{x ^{2} - 2 x - 3}

\frac{19}{6 ( x - 5 )}

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