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

The domain of f(x)=sqrt(1/(3x)+2) is x 0

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

domain

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

x \leq - \frac{1}{6} or x > 0

Interval Notation

(- \infty, - \frac{1}{6}] \cup (0, \infty)

Solution steps

Find non-negative values for radicals:

x \leq - \frac{1}{6} or x > 0

Find undefined (singularity) points:

x = 0

Combine real regions and undefined points for final function domain

x \leq - \frac{1}{6} or x > 0

What is the domain of f(x)=sqrt(1/(3x)+2) ?
The domain of f(x)=sqrt(1/(3x)+2) is x<=-1/6 \lor x>0