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

The domain of f(x)=sqrt((3x^2+x)/(x^2+3x+2)) is x = 0

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

domain

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

x < - 2 or - 1 < x \leq - \frac{1}{3} or x \geq 0

Interval Notation

(- \infty, - 2) \cup (- 1, - \frac{1}{3}] \cup [0, \infty)

Solution steps

Find non-negative values for radicals:

x < - 2 or - 1 < x \leq - \frac{1}{3} or x \geq 0

Find undefined (singularity) points:

x = - 1, x = - 2

Combine real regions and undefined points for final function domain

x < - 2 or - 1 < x \leq - \frac{1}{3} or x \geq 0

5 x + 2 y = 10

f (x) = \frac{7 x - 14}{x ^{2} - 4}

f (x) = - 6 x^{5} + 7 x^{2}

(0, 2), (6, - 7)

3 (x - 4)^{2} + 2

What is the domain of f(x)=sqrt((3x^2+x)/(x^2+3x+2)) ?
The domain of f(x)=sqrt((3x^2+x)/(x^2+3x+2)) is x<-2\lor-1<x<=-1/3 \lor x>= 0