What is the domain of f(x)=(sqrt(x^2+5x+6))/(x+4) ?

The domain of f(x)=(sqrt(x^2+5x+6))/(x+4) is x =-2

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domain of f(x)=(sqrt(x^2+5x+6))/(x+4)

domain

f (x) = \frac{x ^{2} + 5 x + 6}{x + 4}

x < - 4 or - 4 < x \leq - 3 or x \geq - 2

Interval Notation

(- \infty, - 4) \cup (- 4, - 3] \cup [- 2, \infty)

Solution steps

Find non-negative values for radicals:

x \leq - 3 or x \geq - 2

Find undefined (singularity) points:

x = - 4

Combine real regions and undefined points for final function domain

x < - 4 or - 4 < x \leq - 3 or x \geq - 2

f (x) = - lo g_{5} (x - 6) - 3

3 x - \frac{5}{4}

f (x) = \frac{5 + 6 x}{x - 1}

f (x) = 25 - 4 x^{2}

What is the domain of f(x)=(sqrt(x^2+5x+6))/(x+4) ?
The domain of f(x)=(sqrt(x^2+5x+6))/(x+4) is x<-4\lor-4<x<=-3\lor x>=-2