What is the domain of f(x)=(4x)/(x(x^2-16)) ?

The domain of f(x)=(4x)/(x(x^2-16)) is x 4

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domain of f(x)=(4x)/(x(x^2-16))

domain

f (x) = \frac{4 x}{x ( x ^{2} - 16 )}

x < - 4 or - 4 < x < 0 or 0 < x < 4 or x > 4

Interval Notation

(- \infty, - 4) \cup (- 4, 0) \cup (0, 4) \cup (4, \infty)

Solution steps

Find undefined (singularity) points:

x = 0, x = - 4, x = 4

The function domain

x < - 4 or - 4 < x < 0 or 0 < x < 4 or x > 4

What is the domain of f(x)=(4x)/(x(x^2-16)) ?
The domain of f(x)=(4x)/(x(x^2-16)) is x<-4\lor-4<x<0\lor 0<x<4\lor x>4