What is the domain of f(x)= 1/(sqrt(x^2-4x-12)) ?

The domain of f(x)= 1/(sqrt(x^2-4x-12)) is x 6

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domain of f(x)= 1/(sqrt(x^2-4x-12))

domain

f (x) = \frac{1}{x ^{2} - 4 x - 12}

x < - 2 or x > 6

Interval Notation

(- \infty, - 2) \cup (6, \infty)

Solution steps

Find non-negative values for radicals:

x \leq - 2 or x \geq 6

Find undefined (singularity) points:

x = 6, x = - 2

Combine real regions and undefined points for final function domain

x < - 2 or x > 6

f (x) = (x - 2)^{\frac{4}{3}}

e^{x - 6}

(x, - 3), (2, - 6)

f (x) = 48.5 - 2.5 x

(1.3) (7.5)

What is the domain of f(x)= 1/(sqrt(x^2-4x-12)) ?
The domain of f(x)= 1/(sqrt(x^2-4x-12)) is x<-2\lor x>6