What is the domain of f(x)=(sqrt(x+4))/(3x^2+5x+2) ?

The domain of f(x)=(sqrt(x+4))/(3x^2+5x+2) is -4 -2/3

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domain of f(x)=(sqrt(x+4))/(3x^2+5x+2)

domain

f (x) = \frac{x + 4}{3 x ^{2} + 5 x + 2}

- 4 \leq x < - 1 or - 1 < x < - \frac{2}{3} or x > - \frac{2}{3}

Interval Notation

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

Solution steps

Find non-negative values for radicals:

x \geq - 4

Find undefined (singularity) points:

x = - \frac{2}{3}, x = - 1

Combine real regions and undefined points for final function domain

- 4 \leq x < - 1 or - 1 < x < - \frac{2}{3} or x > - \frac{2}{3}

f (x) = 3 e^{x}

y = - x^{4} + 2 x^{2}

f (x) = lo g_{2} (x + 4)

5 x + 6

f (x) = (\frac{1}{2})^{x - 4}

What is the domain of f(x)=(sqrt(x+4))/(3x^2+5x+2) ?
The domain of f(x)=(sqrt(x+4))/(3x^2+5x+2) is -4<= x<-1\lor-1<x<-2/3 \lor x>-2/3