What is the domain of f(x)= 1/(log_{10)(x^2-4)} ?

The domain of f(x)= 1/(log_{10)(x^2-4)} is x sqrt(5)

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domain of f(x)= 1/(log_{10)(x^2-4)}

domain

f (x) = \frac{1}{lo g _{10} ( x ^{2} - 4 )}

x < - 5 or - 5 < x < - 2 or 2 < x < 5 or x > 5

Interval Notation

(- \infty, - 5) \cup (- 5, - 2) \cup (2, 5) \cup (5, \infty)

Solution steps

Find positive values for logs:

x < - 2 or x > 2

Find undefined (singularity) points:

x = 5, x = - 5

Combine real regions and undefined points for final function domain

x < - 5 or - 5 < x < - 2 or 2 < x < 5 or x > 5

What is the domain of f(x)= 1/(log_{10)(x^2-4)} ?
The domain of f(x)= 1/(log_{10)(x^2-4)} is x<-sqrt(5)\lor-sqrt(5)<x<-2\lor 2<x<sqrt(5)\lor x>sqrt(5)