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Is |x^3-1| one to one?

  1. Nov 24, 2012 #1
    1. The problem statement, all variables and given/known data

    Is the function |x^3-1| one to one? Is it monotonous?

    2. Relevant equations

    3. The attempt at a solution

    Since |x^3-1|=|y^3-1| does not necessarily imply that x=y for every x and y, I presume it is not one to one. Hence it has no inverse function.
    It is also not monotonous.
    Are all these statements correct?
  2. jcsd
  3. Nov 24, 2012 #2


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  4. Nov 24, 2012 #3
    Hi tiny-tim,
    Once again, thanks a lot! :-)
  5. Nov 24, 2012 #4


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    While the statements are correct, they are not sufficient to complete the exercise. To actually solve it, you need to find counterexamples. For example, if you want to show that [itex]|x^3-1|[/itex] is not one-to-one, you need to come up with two particular and distinct points x and y such that [itex]|x^3-1|=|y^3-1|[/itex]. Just saying that it is one-to-one is not enough without counterexample.
  6. Nov 24, 2012 #5
    Have done so, simply didn't specify it :-). Thank you, micromass!
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