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

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

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

domain

f (x) = \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) = (5 - x) (2 x - 3)

f (x) = \frac{x ^{7}}{7} + 2

f (x) = \frac{1}{3} x + 4

4 x + 9

f (x) = 4 x - 2

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