What is the domain of f(x)=(2x^2)/(x^3-2x^2-8x) ?

The domain of f(x)=(2x^2)/(x^3-2x^2-8x) is x 4

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domain of f(x)=(2x^2)/(x^3-2x^2-8x)

domain

f (x) = \frac{2 x ^{2}}{x ^{3} - 2 x ^{2} - 8 x}

x < - 2 or - 2 < x < 0 or 0 < x < 4 or x > 4

Interval Notation

(- \infty, - 2) \cup (- 2, 0) \cup (0, 4) \cup (4, \infty)

Solution steps

Find undefined (singularity) points:

x = 0, x = - 2, x = 4

The function domain

x < - 2 or - 2 < x < 0 or 0 < x < 4 or x > 4

f (x) = \frac{6 x}{x - 2}

2 sin (2 x)

7 x + 7

\frac{7}{\frac{7}{x - 6} - 6}

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

What is the domain of f(x)=(2x^2)/(x^3-2x^2-8x) ?
The domain of f(x)=(2x^2)/(x^3-2x^2-8x) is x<-2\lor-2<x<0\lor 0<x<4\lor x>4