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

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

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

domain

f (x) = \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

6 t^{2} + 500 t + 8000

f (x) = - 2 x (x - 2) (x - 5)

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

f (t) = \frac{1}{t}

e^{a r c s i n (x)}

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