What is the domain of f(x)=(5x^3-9)/(x^3+13x^2+42x) ?

The domain of f(x)=(5x^3-9)/(x^3+13x^2+42x) is x 0

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domain of f(x)=(5x^3-9)/(x^3+13x^2+42x)

domain

f (x) = \frac{5 x ^{3} - 9}{x ^{3} + 13 x ^{2} + 42 x}

x < - 7 or - 7 < x < - 6 or - 6 < x < 0 or x > 0

Interval Notation

(- \infty, - 7) \cup (- 7, - 6) \cup (- 6, 0) \cup (0, \infty)

Solution steps

Find undefined (singularity) points:

x = 0, x = - 6, x = - 7

The function domain

x < - 7 or - 7 < x < - 6 or - 6 < x < 0 or x > 0

f (x) = 4^{x}

(8, - 5), (4, 3)

2^{x - 2}

(12, 5), (- 12, - 2)

f (x) = 10 \cdot (\frac{43 + x}{4000})

What is the domain of f(x)=(5x^3-9)/(x^3+13x^2+42x) ?
The domain of f(x)=(5x^3-9)/(x^3+13x^2+42x) is x<-7\lor-7<x<-6\lor-6<x<0\lor x>0