What is the domain of f(x)=(4x^2+7x+27)/((x-3)(x+4)) ?

The domain of f(x)=(4x^2+7x+27)/((x-3)(x+4)) is x 3

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domain of f(x)=(4x^2+7x+27)/((x-3)(x+4))

domain

f (x) = \frac{4 x ^{2} + 7 x + 27}{( x - 3 ) ( x + 4 )}

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)=(4x^2+7x+27)/((x-3)(x+4)) ?
The domain of f(x)=(4x^2+7x+27)/((x-3)(x+4)) is x<-4\lor-4<x<3\lor x>3