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

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

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

domain

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

- 3 < x \leq 0 or x > 3

Interval Notation

(- 3, 0] \cup (3, \infty)

Solution steps

Find non-negative values for radicals:

- 3 < x \leq 0 or x > 3

Find undefined (singularity) points:

x = 3, x = - 3

Combine real regions and undefined points for final function domain

- 3 < x \leq 0 or x > 3

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

x^{2} - x - 2

10 x - y = - 7

(- 1, 6), (2, 8)

f (x) = 3 (x)^{2}

What is the domain of f(x)=sqrt(x/(x^2-9)) ?
The domain of f(x)=sqrt(x/(x^2-9)) is -3<x<= 0\lor x>3