What is the domain of f(x)=(6x)/(x^2+7x+12) ?

The domain of f(x)=(6x)/(x^2+7x+12) is x -3

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domain of f(x)=(6x)/(x^2+7x+12)

domain

f (x) = \frac{6 x}{x ^{2} + 7 x + 12}

x < - 4 or - 4 < x < - 3 or x > - 3

Interval Notation

(- \infty, - 4) \cup (- 4, - 3) \cup (- 3, \infty)

Solution steps

Find undefined (singularity) points:

x = - 3, x = - 4

The function domain

x < - 4 or - 4 < x < - 3 or x > - 3

What is the domain of f(x)=(6x)/(x^2+7x+12) ?
The domain of f(x)=(6x)/(x^2+7x+12) is x<-4\lor-4<x<-3\lor x>-3