What is the domain of f(x)=(x^3+2x^2-15x)/(18x-2x^3) ?

The domain of f(x)=(x^3+2x^2-15x)/(18x-2x^3) is x 3

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domain of f(x)=(x^3+2x^2-15x)/(18x-2x^3)

domain

f (x) = \frac{x ^{3} + 2 x ^{2} - 15 x}{18 x - 2 x ^{3}}

x < - 3 or - 3 < x < 0 or 0 < x < 3 or x > 3

Interval Notation

(- \infty, - 3) \cup (- 3, 0) \cup (0, 3) \cup (3, \infty)

Solution steps

Find undefined (singularity) points:

x = 0, x = - 3, x = 3

The function domain

x < - 3 or - 3 < x < 0 or 0 < x < 3 or x > 3

y = 2 x - 3

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

f (x) = ∣ 2 - x ∣ - 3, - 3 < x \leq 0

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

f (x) = x + 2 + 2

What is the domain of f(x)=(x^3+2x^2-15x)/(18x-2x^3) ?
The domain of f(x)=(x^3+2x^2-15x)/(18x-2x^3) is x<-3\lor-3<x<0\lor 0<x<3\lor x>3