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

The domain of-(x+1)/(|x+1|sqrt(-x^2-2x)) is -2<x<-1\lor-1<x<0

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

domain

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

- 2 < x < - 1 or - 1 < x < 0

Interval Notation

(- 2, - 1) \cup (- 1, 0)

Solution steps

Find non-negative values for radicals:

- 2 \leq x \leq 0

Find undefined (singularity) points:

x = - 1, x = - 2, x = 0

Combine real regions and undefined points for final function domain

- 2 < x < - 1 or - 1 < x < 0

f (x) = \frac{x - 2}{x ^{2} - 3}

f (x) = x^{2} + 7 x - 3

f (x) = - 9

\frac{x ^{2}}{x ^{2} + 16}

f (x) = ln (2 x^{2} + x + 1)

What is the domain of-(x+1)/(|x+1|sqrt(-x^2-2x)) ?
The domain of-(x+1)/(|x+1|sqrt(-x^2-2x)) is -2<x<-1\lor-1<x<0