What is the domain of f(x)=(ln(x^2-9))/(x^2-16) ?

The domain of f(x)=(ln(x^2-9))/(x^2-16) is x 4

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domain of f(x)=(ln(x^2-9))/(x^2-16)

domain

x < - 4 or - 4 < x < - 3 or 3 < x < 4 or x > 4

Interval Notation

(- \infty, - 4) \cup (- 4, - 3) \cup (3, 4) \cup (4, \infty)

Solution steps

Find positive values for logs:

x < - 3 or x > 3

Find undefined (singularity) points:

x = 4, x = - 4

Combine real regions and undefined points for final function domain

x < - 4 or - 4 < x < - 3 or 3 < x < 4 or x > 4

What is the domain of f(x)=(ln(x^2-9))/(x^2-16) ?
The domain of f(x)=(ln(x^2-9))/(x^2-16) is x<-4\lor-4<x<-3\lor 3<x<4\lor x>4