What is the domain of f(x)=(x-13)/(sqrt(x^2-x-6)) ?

The domain of f(x)=(x-13)/(sqrt(x^2-x-6)) is x 3

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domain of f(x)=(x-13)/(sqrt(x^2-x-6))

domain

f (x) = \frac{x - 13}{x ^{2} - x - 6}

x < - 2 or x > 3

Interval Notation

(- \infty, - 2) \cup (3, \infty)

Solution steps

Find non-negative values for radicals:

x \leq - 2 or x \geq 3

Find undefined (singularity) points:

x = 3, x = - 2

Combine real regions and undefined points for final function domain

x < - 2 or x > 3

What is the domain of f(x)=(x-13)/(sqrt(x^2-x-6)) ?
The domain of f(x)=(x-13)/(sqrt(x^2-x-6)) is x<-2\lor x>3