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

\frac{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}

\frac{1}{x + 5} + 3

f (x) = 3 + 2 ln (x - 1)

x^{3} + 2 x^{2} + x - 7

y = - x^{2} + 8 x - 17

f (x) = 9 - x^{2} + x + 1

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