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

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

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domain of sqrt(1-2x)+1/x

domain

1 - 2 x + \frac{1}{x}

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

Interval Notation

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

Solution steps

Find non-negative values for radicals:

x \leq \frac{1}{2}

Find undefined (singularity) points:

x = 0

Combine real regions and undefined points for final function domain

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

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