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

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

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domain of sqrt(1/x+2)

domain

\frac{1}{x} + 2

x \leq - \frac{1}{2} or x > 0

Interval Notation

(- \infty, - \frac{1}{2}] \cup (0, \infty)

Solution steps

Find non-negative values for radicals:

x \leq - \frac{1}{2} or x > 0

Find undefined (singularity) points:

x = 0

Combine real regions and undefined points for final function domain

x \leq - \frac{1}{2} or x > 0

f (x) = \frac{x ^{3}}{27}

0

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

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

x^{2} - 6 x

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