What is the domain of f(x)=(sqrt(x+2))/(3x^2+7x+4) ?

The domain of f(x)=(sqrt(x+2))/(3x^2+7x+4) is -2 -1

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domain of f(x)=(sqrt(x+2))/(3x^2+7x+4)

domain

f (x) = \frac{x + 2}{3 x ^{2} + 7 x + 4}

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

Interval Notation

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

Solution steps

Find non-negative values for radicals:

x \geq - 2

Find undefined (singularity) points:

x = - 1, x = - \frac{4}{3}

Combine real regions and undefined points for final function domain

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

f (x) = 2^{x + 1} - 2

\frac{x + 4}{5}

f (x) = x^{2} - 7 x + 12

\frac{7 x}{x + 2}

f (x) = 2 x^{3} - 3 x^{2} + 6, - 1 \leq x \leq 1

What is the domain of f(x)=(sqrt(x+2))/(3x^2+7x+4) ?
The domain of f(x)=(sqrt(x+2))/(3x^2+7x+4) is -2<= x<-4/3 \lor-4/3 <x<-1\lor x>-1