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Question about strictly increasing

  1. Aug 2, 2012 #1
    1. The problem statement, all variables and given/known data
    Hello, Does anybody know how to solve this question? Or a formal way to prove that a fuction is strictly increasing?

    Define f(x)={ x-1 if x<0
    x+1 if x >_ 0

    Show that f: R -> R is strictly increasing and that f^(-1) : f(R) -> R is continuous at 1


    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Aug 2, 2012 #2

    SammyS

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    Hello nikefish. Welcome to PF !

    What have you tried ?

    Where are you stuck ?



    What is your definition of a strictly increasing function ?

    .
     
  4. Aug 2, 2012 #3

    HallsofIvy

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    The first thing you should do is graph the function.
     
  5. Aug 2, 2012 #4
    Use the definition of "strictly increasing" to show part 1 and use the definition of "continuous" for part 2.

     
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