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

The domain of f(y)=ln|(x+1)/(x-1)| is x 1

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

domain

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

x < - 1 or - 1 < x < 1 or x > 1

Interval Notation

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

Solution steps

Find positive values for logs:

x < - 1 or - 1 < x < 1 or x > 1

Find undefined (singularity) points:

x = 1

Combine real regions and undefined points for final function domain

x < - 1 or - 1 < x < 1 or x > 1

f (x) = x^{2} + 10 x + 16

f (x) = x^{3} + 4 x^{2} - 2 x - 6

\frac{76}{x - 4}

\frac{( x - 3 )}{( 2 x - 7 )}

- x - 4

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