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

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

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domain of f(x)=ln(((|x|-1))/(x^2-2))

domain

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

x < - 2 or - 1 < x < 1 or x > 2

Interval Notation

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

Solution steps

Find positive values for logs:

x < - 2 or - 1 < x < 1 or x > 2

Find undefined (singularity) points:

x = 2, x = - 2

Combine real regions and undefined points for final function domain

x < - 2 or - 1 < x < 1 or x > 2

f (x) = \frac{3}{x - 13}

2 x^{2} + 5 x + 10

y = x^{2} + 4 x + 2

f (x) = \frac{x - 8}{x ^{2} - 64}

y = 1 - x^{2}

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