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

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

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

domain

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

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

Interval Notation

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

Solution steps

Find non-negative values for radicals:

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

Find undefined (singularity) points:

x = 2, x = - 2

Combine real regions and undefined points for final function domain

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

g (x) = \frac{1}{x - 9}

f (x) = - (x + 2)^{5} (x - 4)^{4}

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

f (x) = \frac{3 - x}{∣ 2 x - 5 ∣}

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