What is the domain of f(x)=(|x|-2)/(sqrt(x^2-2x-3)) ?

The domain of f(x)=(|x|-2)/(sqrt(x^2-2x-3)) is x 3

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domain of f(x)=(|x|-2)/(sqrt(x^2-2x-3))

domain

f (x) = \frac{∣ x ∣ - 2}{x ^{2} - 2 x - 3}

x < - 1 or x > 3

Interval Notation

(- \infty, - 1) \cup (3, \infty)

Solution steps

Find non-negative values for radicals:

x \leq - 1 or x \geq 3

Find undefined (singularity) points:

x = 3, x = - 1

Combine real regions and undefined points for final function domain

x < - 1 or x > 3

What is the domain of f(x)=(|x|-2)/(sqrt(x^2-2x-3)) ?
The domain of f(x)=(|x|-2)/(sqrt(x^2-2x-3)) is x<-1\lor x>3