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

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

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

domain

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

x < - 3 or - 3 < x < 0 or 0 < x < 3 or x > 3

Interval Notation

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

Solution steps

Find undefined (singularity) points:

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

The function domain

x < - 3 or - 3 < x < 0 or 0 < x < 3 or x > 3

f (x) = \frac{5}{x ^{2}}

\frac{x + 7}{x - 5}

f (x) = 25 - x^{2} - 2

f (x) = ln (1 + x)

f (x) = \frac{x - 7}{4}

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