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

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

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

domain

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

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

Interval Notation

(- \infty, - 1) \cup (- 1, 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, x = 1, x = - 1

Combine real regions and undefined points for final function domain

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

f (x) = lo g_{4} (\frac{1}{4} x - 12)

ln (3 x + 4)

f (x) = \frac{3 x + 2}{x - 2}

f (x) = x + 1, x < - 1

f (x) = \frac{4 x}{- 3 x + 11}

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