What is the domain of f(x)= 5/(ln(x^2-1)) ?

The domain of f(x)= 5/(ln(x^2-1)) is x sqrt(2)

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domain of f(x)= 5/(ln(x^2-1))

domain

f (x) = \frac{5}{ln ( x ^{2} - 1 )}

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

Interval Notation

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

Solution steps

Find positive values for logs:

x < - 1 or x > 1

Find undefined (singularity) points:

x = 2, x = - 2

Combine real regions and undefined points for final function domain

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

\frac{2 x + 18}{x + 1}

f (x) = \frac{x + 6}{x ^{2} + 6 x - 27}

f (x) = - x + 1 + ln (x)

g (x) = 5^{x}

f (x) = \frac{1}{x - 2} g (x) = \frac{8}{x + 3}

What is the domain of f(x)= 5/(ln(x^2-1)) ?
The domain of f(x)= 5/(ln(x^2-1)) is x<-sqrt(2)\lor-sqrt(2)<x<-1\lor 1<x<sqrt(2)\lor x>sqrt(2)