What is the domain of f(x)=(3x)/(2x^3-x^2-15x) ?

The domain of f(x)=(3x)/(2x^3-x^2-15x) is x 3

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domain of f(x)=(3x)/(2x^3-x^2-15x)

domain

f (x) = \frac{3 x}{2 x ^{3} - x ^{2} - 15 x}

x < - \frac{5}{2} or - \frac{5}{2} < x < 0 or 0 < x < 3 or x > 3

Interval Notation

(- \infty, - \frac{5}{2}) \cup (- \frac{5}{2}, 0) \cup (0, 3) \cup (3, \infty)

Solution steps

Find undefined (singularity) points:

x = 0, x = - \frac{5}{2}, x = 3

The function domain

x < - \frac{5}{2} or - \frac{5}{2} < x < 0 or 0 < x < 3 or x > 3

f (x) = \frac{x + 3}{x ^{2} + 8 x + 15}

F (X) = \frac{1}{X ^{3 - 2 X^{2} - 15 X}}

\frac{5}{x ^{4} - 16}

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

f (x) = \frac{x - 2}{4 x ^{2} - 9}

What is the domain of f(x)=(3x)/(2x^3-x^2-15x) ?
The domain of f(x)=(3x)/(2x^3-x^2-15x) is x<-5/2 \lor-5/2 <x<0\lor 0<x<3\lor x>3