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

The domain of y=(-|x|+4)/(sqrt(x^2+x)) is x 0

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domain of y=(-|x|+4)/(sqrt(x^2+x))

domain

y = \frac{- ∣ x ∣ + 4}{x ^{2} + x}

x < - 1 or x > 0

Interval Notation

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

Solution steps

Find non-negative values for radicals:

x \leq - 1 or x \geq 0

Find undefined (singularity) points:

x = 0, x = - 1

Combine real regions and undefined points for final function domain

x < - 1 or x > 0

f (x) = - 2 x^{2} - 12 x + 13

f (x) = (x^{3} - 1)

f (x) = x^{2} - 8 x + 15

f (x) = \frac{1 + x ^{2}}{x ^{2} - x ^{4}}

What is the domain of y=(-|x|+4)/(sqrt(x^2+x)) ?
The domain of y=(-|x|+4)/(sqrt(x^2+x)) is x<-1\lor x>0