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

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

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

domain

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

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