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

The domain of sqrt(x^2-x-2)+(x+1)/(x^2-4) is x 2

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domain of sqrt(x^2-x-2)+(x+1)/(x^2-4)

domain

x^{2} - x - 2 + \frac{x + 1}{x ^{2} - 4}

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

Interval Notation

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

Solution steps

Find non-negative values for radicals:

x \leq - 1 or x \geq 2

Find undefined (singularity) points:

x = 2, x = - 2

Combine real regions and undefined points for final function domain

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

f (x) = \frac{( x + 2 )}{2}

f (x) = x^{1000}

cot (x + \frac{7 π}{36})

f (x) = 3 x^{2} + 2

(5, 6), (3, - 2)

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