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

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

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

domain

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

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

Interval Notation

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

Solution steps

Find non-negative values for radicals:

x \leq - 1 or x \geq 1

Find undefined (singularity) points:

x = - 2

Combine real regions and undefined points for final function domain

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

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