What is the domain of f(x)=(sqrt(x+5))/(3x^2+10x+3) ?

The domain of f(x)=(sqrt(x+5))/(3x^2+10x+3) is -5 -1/3

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domain of f(x)=(sqrt(x+5))/(3x^2+10x+3)

domain

f (x) = \frac{x + 5}{3 x ^{2} + 10 x + 3}

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

Interval Notation

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

Solution steps

Find non-negative values for radicals:

x \geq - 5

Find undefined (singularity) points:

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

Combine real regions and undefined points for final function domain

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

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

f (x) = 2 x - 6 - 1

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

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

y = \frac{1}{x + 1}

What is the domain of f(x)=(sqrt(x+5))/(3x^2+10x+3) ?
The domain of f(x)=(sqrt(x+5))/(3x^2+10x+3) is -5<= x<-3\lor-3<x<-1/3 \lor x>-1/3