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

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

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

domain

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

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

4 - z^{2}

\frac{x ^{3} + 7 x ^{2} + 12 x}{x ^{3} + x ^{2} - 2 x}

f (x) = (x + 16)^{3}

f (x) = \frac{x ^{2} - 4}{x - 1}

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

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