find the range of mod(x-1)/x-1
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Originally Posted by prasum find the range of mod(x-1)/x-1 Make a sketch of $\displaystyle f(x)=(x-1)/(x+1)=1-(2/(x+1))$ and by symmetry, of $\displaystyle |f(x)|$ . You'll easily find $\displaystyle \textrm {rg} (|f|)=[0,+\infty)$ .
it is x-1 not x+1
Originally Posted by prasum it is x-1 not x+1 Sorry, my bad. What have you tried so far?.
Originally Posted by prasum find the range of mod(x-1)/x-1 Please use brackets so we do not need to guess that you have left essential brackets out. CB
Originally Posted by prasum find the range of mod(x-1)/x-1 |x-1|/(x-1)=|x-1|/(sgn(x-1) |x-1|)=sgn(x-1), assuming x is not equal to 1. CB
If the OP meant $\displaystyle f(x)=\mod (x-1/x-1)$ then, $\displaystyle f(x)=1$ for all $\displaystyle x\neq 1$ and $\displaystyle \textrm{rg}(f)=\{1\}$ . P.S. Of course, it seems to be mod(x-1)/(x-1).
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