1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

  4. Nov 24, 2012 #3
    Hi tiny-tim,
    Once again, thanks a lot! :-)
     
  5. Nov 24, 2012 #4
    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!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook