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

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

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domain of f(x)=sqrt(|(x-1)/(x+1)|-1)

domain

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

x < - 1 or - 1 < x \leq 0

Interval Notation

(- \infty, - 1) \cup (- 1, 0]

Solution steps

Find non-negative values for radicals:

x < - 1 or - 1 < x \leq 0

Find undefined (singularity) points:

x = - 1

Combine real regions and undefined points for final function domain

x < - 1 or - 1 < x \leq 0

f (x) = 2 + n cos (x)

\frac{2 x + 3}{2 x ^{2} + x - 1}

f (x) = (\frac{7 x}{x - 5})

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

f (x) = \frac{x ^{2} + 2 x - 3}{x ^{2} + 5 x + 6}

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