What is the domain of f(x)=(x^3+x^2-2x)/(-3x^2+27) ?

The domain of f(x)=(x^3+x^2-2x)/(-3x^2+27) is x 3

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domain of f(x)=(x^3+x^2-2x)/(-3x^2+27)

domain

f (x) = \frac{x ^{3} + x ^{2} - 2 x}{- 3 x ^{2} + 27}

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

Interval Notation

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

Solution steps

Find undefined (singularity) points:

x = 3, x = - 3

The function domain

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

11

f (x) = - 3 - 4 x - 12

\frac{1}{9 - x - 3}

f (x) = x^{2} - x + 6 + 1

\frac{x - 6}{x ^{2} - 16}

What is the domain of f(x)=(x^3+x^2-2x)/(-3x^2+27) ?
The domain of f(x)=(x^3+x^2-2x)/(-3x^2+27) is x<-3\lor-3<x<3\lor x>3