What is the domain of f(x)=(x^2-2x)/(x^3-16x) ?

The domain of f(x)=(x^2-2x)/(x^3-16x) is x 4

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domain of f(x)=(x^2-2x)/(x^3-16x)

domain

f (x) = \frac{x ^{2} - 2 x}{x ^{3} - 16 x}

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

f (x) = - x^{2} - 2 x - 4

f (x) = x^{2} + 8

f (x) = 2 x^{2} - 12 x + 16

5 x^{4} - 2 x^{2} + 2 x

f (x) = \frac{2}{\frac{3}{x - 1}}

What is the domain of f(x)=(x^2-2x)/(x^3-16x) ?
The domain of f(x)=(x^2-2x)/(x^3-16x) is x<-4\lor-4<x<0\lor 0<x<4\lor x>4