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

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

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

domain

f (x) = \frac{1}{3 x - 2 - 2}

\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

Combine real regions and undefined points for final function domain

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

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