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

\frac{∣ x - 2 ∣ - 1}{[ x + 3 ] + 2}

- 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

y = \frac{x + 6}{15 - x ^{2} - 64}

(x + 3) 2 - 2

7 x^{2} - 10 x + 5

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

y = \frac{- ∣ x ∣ + 4}{x ^{2} + x}

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