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

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

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

domain

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

x > - \frac{2}{3}

Interval Notation

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

Solution steps

Find non-negative values for radicals:

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

Find undefined (singularity) points:

x = - \frac{2}{3}

Combine real regions and undefined points for final function domain

x > - \frac{2}{3}

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