What is the domain of f(x)=(x+2)/(sqrt(4x-x^3)) ?

The domain of f(x)=(x+2)/(sqrt(4x-x^3)) is x<-2\lor 0<x<2

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domain of f(x)=(x+2)/(sqrt(4x-x^3))

domain

f (x) = \frac{x + 2}{4 x - x ^{3}}

x < - 2 or 0 < x < 2

Interval Notation

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

Solution steps

Find non-negative values for radicals:

x \leq - 2 or 0 \leq x \leq 2

Find undefined (singularity) points:

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

Combine real regions and undefined points for final function domain

x < - 2 or 0 < x < 2

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

\frac{x - 2}{3}

\frac{x}{8 x - 7}

f (x) = \frac{1}{( 1 - x + 5 )}

\frac{- 1}{x - 2}

What is the domain of f(x)=(x+2)/(sqrt(4x-x^3)) ?
The domain of f(x)=(x+2)/(sqrt(4x-x^3)) is x<-2\lor 0<x<2