What is the domain of f(x)= 5/(x^3+10x^2+9x) ?

The domain of f(x)= 5/(x^3+10x^2+9x) is x 0

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domain of f(x)= 5/(x^3+10x^2+9x)

domain

f (x) = \frac{5}{x ^{3} + 10 x ^{2} + 9 x}

x < - 9 or - 9 < x < - 1 or - 1 < x < 0 or x > 0

Interval Notation

(- \infty, - 9) \cup (- 9, - 1) \cup (- 1, 0) \cup (0, \infty)

Solution steps

Find undefined (singularity) points:

x = 0, x = - 1, x = - 9

The function domain

x < - 9 or - 9 < x < - 1 or - 1 < x < 0 or x > 0

What is the domain of f(x)= 5/(x^3+10x^2+9x) ?
The domain of f(x)= 5/(x^3+10x^2+9x) is x<-9\lor-9<x<-1\lor-1<x<0\lor x>0