What is the domain of f(x)=sqrt((x-2)/(3x^2+8x+4)) ?

The domain of f(x)=sqrt((x-2)/(3x^2+8x+4)) is -2 = 2

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domain of f(x)=sqrt((x-2)/(3x^2+8x+4))

domain

f (x) = \frac{x - 2}{3 x ^{2} + 8 x + 4}

- 2 < x < - \frac{2}{3} or x \geq 2

Interval Notation

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

Solution steps

Find non-negative values for radicals:

- 2 < x < - \frac{2}{3} or x \geq 2

Find undefined (singularity) points:

x = - \frac{2}{3}, x = - 2

Combine real regions and undefined points for final function domain

- 2 < x < - \frac{2}{3} or x \geq 2

d o main f (x) = - 3 x + 4

a sy m pt o t es f (x) = \frac{2 x ^{2} - 6 x + 1}{1 + x ^{2}}

f (x) = (sin (x))^{2}

mi d p o in t (- 9, - 8), (- 5, 6)

in t erce pt s y = x - 3

What is the domain of f(x)=sqrt((x-2)/(3x^2+8x+4)) ?
The domain of f(x)=sqrt((x-2)/(3x^2+8x+4)) is -2<x<-2/3 \lor x>= 2