What is the domain of f(x)=(sqrt(x^2-4))/(x^2+x-12) ?

The domain of f(x)=(sqrt(x^2-4))/(x^2+x-12) is x 3

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domain of f(x)=(sqrt(x^2-4))/(x^2+x-12)

domain

x < - 4 or - 4 < x \leq - 2 or 2 \leq x < 3 or x > 3

Interval Notation

(- \infty, - 4) \cup (- 4, - 2] \cup [2, 3) \cup (3, \infty)

Solution steps

Find non-negative values for radicals:

x \leq - 2 or x \geq 2

Find undefined (singularity) points:

x = 3, x = - 4

Combine real regions and undefined points for final function domain

x < - 4 or - 4 < x \leq - 2 or 2 \leq x < 3 or x > 3

What is the domain of f(x)=(sqrt(x^2-4))/(x^2+x-12) ?
The domain of f(x)=(sqrt(x^2-4))/(x^2+x-12) is x<-4\lor-4<x<=-2\lor 2<= x<3\lor x>3