What is the domain of f(x)=(3x+4)/(x^2+7x+12) ?

The domain of f(x)=(3x+4)/(x^2+7x+12) is x -3

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domain of f(x)=(3x+4)/(x^2+7x+12)

domain

f (x) = \frac{3 x + 4}{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

arccos (e^{3 x})

f (x) = - 3 (x - 1)^{2} + 2

x - 4 \cdot \frac{3}{x - 1}

f (x) = 3 \frac{3 x + 2}{x ^{2} + 1}

f (x) = \frac{12}{x ^{2} - 25} - 3

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