What is the domain of f(x)=(2x)/(2x^3+x^2-10x) ?

The domain of f(x)=(2x)/(2x^3+x^2-10x) is x 2

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domain of f(x)=(2x)/(2x^3+x^2-10x)

domain

f (x) = \frac{2 x}{2 x ^{3} + x ^{2} - 10 x}

x < - \frac{5}{2} or - \frac{5}{2} < x < 0 or 0 < x < 2 or x > 2

Interval Notation

(- \infty, - \frac{5}{2}) \cup (- \frac{5}{2}, 0) \cup (0, 2) \cup (2, \infty)

Solution steps

Find undefined (singularity) points:

x = 0, x = 2, x = - \frac{5}{2}

The function domain

x < - \frac{5}{2} or - \frac{5}{2} < x < 0 or 0 < x < 2 or x > 2

f (x) = \frac{3 x + 6}{x ^{2} - x - 2}

f (x) = 10 - x + x^{2} - 9

\frac{1}{x ^{4} + 4 x ^{2} - 1}

\frac{- x + 1}{3 x + 6}

f (x) = \frac{2 x - 1}{2 x - 6}

What is the domain of f(x)=(2x)/(2x^3+x^2-10x) ?
The domain of f(x)=(2x)/(2x^3+x^2-10x) is x<-5/2 \lor-5/2 <x<0\lor 0<x<2\lor x>2