What is the domain of f(x)= 1/(sqrt(x^2-2x-8)) ?

The domain of f(x)= 1/(sqrt(x^2-2x-8)) is x 4

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domain of f(x)= 1/(sqrt(x^2-2x-8))

domain

x < - 2 or x > 4

Interval Notation

(- \infty, - 2) \cup (4, \infty)

Solution steps

Find non-negative values for radicals:

x \leq - 2 or x \geq 4

Find undefined (singularity) points:

x = 4, x = - 2

Combine real regions and undefined points for final function domain

x < - 2 or x > 4

What is the domain of f(x)= 1/(sqrt(x^2-2x-8)) ?
The domain of f(x)= 1/(sqrt(x^2-2x-8)) is x<-2\lor x>4