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

The domain of y=sqrt(x/(4-x^2)) is x<-2\lor 0<= x<2

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

domain

y = \frac{x}{4 - x ^{2}}

x < - 2 or 0 \leq x < 2

Interval Notation

(- \infty, - 2) \cup [0, 2)

Solution steps

Find non-negative values for radicals:

x < - 2 or 0 \leq x < 2

Find undefined (singularity) points:

x = 2, x = - 2

Combine real regions and undefined points for final function domain

x < - 2 or 0 \leq x < 2

f (x) = \frac{- 2 x + 4}{x - 6}

5 x - 15

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

5 x^{3} - 6

2000 x - 5 x^{2}

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