what is the range of the function f(x) = I x- 1I /x-1

The question should be; 
what is the range of the function f(x) = I x- 1I /x-1

​​​​​​​Let y = x-1x-1As we know that x=x if x>0-x if x<0So here x-1=x -1if x-1>0-x-1 if x-1<0So y = x-1x-1=x -1x-1if x-1>0-x-1x-1 if x-1<0=1 if x-1>0-1 if x-1<0So range is 1,-1Now y =  x-1x-1 is not defined for x = 1 so domain is x R-1

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Range is {-1,1}
Domain is R-{1}
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