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

The domain of f(x)=sqrt((3x^2+3)/(x^2+3x+2)) is x -1

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domain of f(x)=sqrt((3x^2+3)/(x^2+3x+2))

domain

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

x < - 2 or x > - 1

Interval Notation

(- \infty, - 2) \cup (- 1, \infty)

Solution steps

Find non-negative values for radicals:

x < - 2 or x > - 1

Find undefined (singularity) points:

x = - 1, x = - 2

Combine real regions and undefined points for final function domain

x < - 2 or x > - 1

f (x) = ln (x^{2} - x - 2)

f (x) = - 2 (x + 5)^{2} - 3

y = - 1

y = \frac{x}{x ^{2} + 16}

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What is the domain of f(x)=sqrt((3x^2+3)/(x^2+3x+2)) ?
The domain of f(x)=sqrt((3x^2+3)/(x^2+3x+2)) is x<-2\lor x>-1