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

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

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

domain

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

x \leq - \frac{1}{3} or x > 0

Interval Notation

(- \infty, - \frac{1}{3}] \cup (0, \infty)

Solution steps

Find non-negative values for radicals:

x \leq - \frac{1}{3} or x > 0

Find undefined (singularity) points:

x = 0

Combine real regions and undefined points for final function domain

x \leq - \frac{1}{3} or x > 0

f (x) = x^{2} + 25

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

f (x) = sec (x) - \frac{1}{x ^{3}} + 5

f (x) = 8 (x^{7} + 8)^{\frac{1}{2}}

(0, \frac{1}{2}), (- \frac{2}{3}, 0)

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