What is the domain of f(x)=(3x^2-8)/(sqrt(x^2+5x+6)) ?

The domain of f(x)=(3x^2-8)/(sqrt(x^2+5x+6)) is x -2

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domain of f(x)=(3x^2-8)/(sqrt(x^2+5x+6))

domain

f (x) = \frac{3 x ^{2} - 8}{x ^{2} + 5 x + 6}

x < - 3 or x > - 2

Interval Notation

(- \infty, - 3) \cup (- 2, \infty)

Solution steps

Find non-negative values for radicals:

x \leq - 3 or x \geq - 2

Find undefined (singularity) points:

x = - 2, x = - 3

Combine real regions and undefined points for final function domain

x < - 3 or x > - 2

What is the domain of f(x)=(3x^2-8)/(sqrt(x^2+5x+6)) ?
The domain of f(x)=(3x^2-8)/(sqrt(x^2+5x+6)) is x<-3\lor x>-2