What is the domain of f(x)=sqrt((x-3)/(9x-x^3)) ?

The domain of f(x)=sqrt((x-3)/(9x-x^3)) is -3<x<0

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domain of f(x)=sqrt((x-3)/(9x-x^3))

domain

f (x) = \frac{x - 3}{9 x - x ^{3}}

- 3 < x < 0

Interval Notation

(- 3, 0)

Solution steps

Find non-negative values for radicals:

- 3 < x < 0

Find undefined (singularity) points:

x = 0, x = - 3, x = 3

Combine real regions and undefined points for final function domain

- 3 < x < 0

x^{2} - 5 x - 24

f (x) = 3 x^{3}

\frac{e ^{x}}{x}

y = - \frac{3}{4} x - 5

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

What is the domain of f(x)=sqrt((x-3)/(9x-x^3)) ?
The domain of f(x)=sqrt((x-3)/(9x-x^3)) is -3<x<0