What is the domain of f(x)=(3x-9)/(sqrt(x^2-6x-7)) ?

The domain of f(x)=(3x-9)/(sqrt(x^2-6x-7)) is x 7

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domain of f(x)=(3x-9)/(sqrt(x^2-6x-7))

domain

x < - 1 or x > 7

Interval Notation

(- \infty, - 1) \cup (7, \infty)

Solution steps

Find non-negative values for radicals:

x \leq - 1 or x \geq 7

Find undefined (singularity) points:

x = 7, x = - 1

Combine real regions and undefined points for final function domain

x < - 1 or x > 7

What is the domain of f(x)=(3x-9)/(sqrt(x^2-6x-7)) ?
The domain of f(x)=(3x-9)/(sqrt(x^2-6x-7)) is x<-1\lor x>7