What is the domain of f(x)= 1/(sqrt(3x+2)) ?

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

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domain of f(x)= 1/(sqrt(3x+2))

domain

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

f (x) = \frac{1}{2} (- 4 x + 20)^{2} - 3

f (x) = (x + 8)^{2} - 3

f (x) = - \frac{4 x ^{2}}{3} + 55 x

9 - x^{3}

(9 - x^{2}) (x + 1)

What is the domain of f(x)= 1/(sqrt(3x+2)) ?
The domain of f(x)= 1/(sqrt(3x+2)) is x>-2/3