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Math Help - range

  1. #1
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    range

    find the range of mod(x-1)/x-1
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Quote Originally Posted by prasum View Post
    find the range of mod(x-1)/x-1


    Make a sketch of f(x)=(x-1)/(x+1)=1-(2/(x+1)) and by symmetry, of |f(x)| . You'll easily find \textrm {rg} (|f|)=[0,+\infty) .
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    it is x-1 not x+1
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  4. #4
    MHF Contributor FernandoRevilla's Avatar
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    Quote Originally Posted by prasum View Post
    it is x-1 not x+1

    Sorry, my bad. What have you tried so far?.
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  5. #5
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    Quote Originally Posted by prasum View Post
    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
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  6. #6
    Grand Panjandrum
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    Quote Originally Posted by prasum View Post
    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
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  7. #7
    MHF Contributor FernandoRevilla's Avatar
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    If the OP meant f(x)=\mod (x-1/x-1) then, f(x)=1

    for all x\neq 1 and \textrm{rg}(f)=\{1\} .


    P.S. Of course, it seems to be mod(x-1)/(x-1).
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