What is the domain of f(x)=(x-2)/(x^3-36x) ?

The domain of f(x)=(x-2)/(x^3-36x) is x 6

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domain of f(x)=(x-2)/(x^3-36x)

domain

f (x) = \frac{x - 2}{x ^{3} - 36 x}

x < - 6 or - 6 < x < 0 or 0 < x < 6 or x > 6

Interval Notation

(- \infty, - 6) \cup (- 6, 0) \cup (0, 6) \cup (6, \infty)

Solution steps

Find undefined (singularity) points:

x = 0, x = - 6, x = 6

The function domain

x < - 6 or - 6 < x < 0 or 0 < x < 6 or x > 6

What is the domain of f(x)=(x-2)/(x^3-36x) ?
The domain of f(x)=(x-2)/(x^3-36x) is x<-6\lor-6<x<0\lor 0<x<6\lor x>6