What is the range of the function f(x)=[...

What is the range of the function `f(x)=[|x-1|]/[x-1]`

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Domain=`x in R-{1}`
Range=`y in [{-1}{1}]`
`y=(x-1)/(x-1)=1`
`y=-(x-1)/(x-1)=-1`

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