What is the domain of f(x)=sqrt((x^2+x)/(x^3-9x)) ?

The domain of f(x)=sqrt((x^2+x)/(x^3-9x)) is -3 3

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domain of f(x)=sqrt((x^2+x)/(x^3-9x))

domain

f (x) = \frac{x ^{2} + x}{x ^{3} - 9 x}

- 3 < x \leq - 1 or x > 3

Interval Notation

Solution steps

Find non-negative values for radicals:

- 3 < x \leq - 1 or x > 3

Find undefined (singularity) points:

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

Combine real regions and undefined points for final function domain

- 3 < x \leq - 1 or x > 3

y = 4^{x} - 3 \cdot 2^{x} + 2

f (x) = - \frac{1}{2} (4^{2 (x + 1)}) - 3

f (x) = - x^{3} - 2 x^{2} + 36 x + 72

- sin (x)

arcsin (sin (x))

What is the domain of f(x)=sqrt((x^2+x)/(x^3-9x)) ?
The domain of f(x)=sqrt((x^2+x)/(x^3-9x)) is -3<x<=-1\lor x>3