What is the domain of sqrt((|x-2|-1)/([x+3]+2)) ?

The domain of sqrt((|x-2|-1)/([x+3]+2)) is -5 = 3

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domain of sqrt((|x-2|-1)/([x+3]+2))

domain

- 5 < x \leq 1 or x \geq 3

Interval Notation

(- 5, 1] \cup [3, \infty)

Solution steps

Find non-negative values for radicals:

- 5 < x \leq 1 or x \geq 3

Find undefined (singularity) points:

x = - 5

Combine real regions and undefined points for final function domain

- 5 < x \leq 1 or x \geq 3

What is the domain of sqrt((|x-2|-1)/([x+3]+2)) ?
The domain of sqrt((|x-2|-1)/([x+3]+2)) is -5<x<= 1\lor x>= 3