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

f (x) = \frac{x ^{2} - 4}{x ^{2} + x - 12}

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

sin (x - 4)

f (x) = 7 x^{2} + 1

\frac{2}{3} tan (2 x + π)

\frac{x ^{3} - 6 x ^{2} + 4 x + 8}{x ^{3} - x ^{2} - 9 x + 9}

y = \frac{x ^{2} - x}{x ^{2} - 1}

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