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

The domain of f(x)=(sqrt(x^2-x-2))/(|x|-4) is x 4

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

domain

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

x < - 4 or - 4 < x \leq - 1 or 2 \leq x < 4 or x > 4

Interval Notation

(- \infty, - 4) \cup (- 4, - 1] \cup [2, 4) \cup (4, \infty)

Solution steps

Find non-negative values for radicals:

x \leq - 1 or x \geq 2

Find undefined (singularity) points:

x = - 4, x = 4

Combine real regions and undefined points for final function domain

x < - 4 or - 4 < x \leq - 1 or 2 \leq x < 4 or x > 4

f (x) = \frac{- 6 x - 24}{- 2}

3 (2 x - 4) - 2

f (x) = - \frac{5 - 1 - x}{6}

f (5.5) = 6 x - 1

f (x) = - 0.0625 (5)^{2} + 3 (5) - 20

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