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

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

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

domain

x < - 2 or x > 2

Interval Notation

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

Solution steps

Find non-negative values for radicals:

x \leq - 2 or x \geq 2

Find undefined (singularity) points:

x = 2, x = - 2

Combine real regions and undefined points for final function domain

x < - 2 or x > 2

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