What is the domain of f(x)=(x-5)/((sqrt(x^2-9))) ?

The domain of f(x)=(x-5)/((sqrt(x^2-9))) is x 3

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domain of f(x)=(x-5)/((sqrt(x^2-9)))

domain

x < - 3 or x > 3

Interval Notation

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

Solution steps

Find non-negative values for radicals:

x \leq - 3 or x \geq 3

Find undefined (singularity) points:

x = 3, x = - 3

Combine real regions and undefined points for final function domain

x < - 3 or x > 3

What is the domain of f(x)=(x-5)/((sqrt(x^2-9))) ?
The domain of f(x)=(x-5)/((sqrt(x^2-9))) is x<-3\lor x>3