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

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

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

domain

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

0 < x \leq \frac{1}{2}

Interval Notation

(0, \frac{1}{2}]

Solution steps

Find non-negative values for radicals:

0 < x \leq \frac{1}{2}

Find undefined (singularity) points:

x = 0

Combine real regions and undefined points for final function domain

0 < x \leq \frac{1}{2}

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