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For each real number x, let f(x) be the minimum of the numbers 4x+1,

  1. Aug 31, 2012 #1
    For each real number x, let f(x) be the minimum of the numbers 4x+1, x+2, and -2x+4. What is the maximum value of f(x)?
     
  2. jcsd
  3. Aug 31, 2012 #2

    Mark44

    Staff: Mentor

    Re: Functions.

    Is this a homework problem?
     
  4. Aug 31, 2012 #3
    Re: Functions.

    No, Sir.
    It is too taken from The Advanced Mathematical Thinking where the author said it can be solved by reversal tactic.

    Sorry if it is incomplete since I copied whatever written in the book.
     
  5. Aug 31, 2012 #4

    Bacle2

    User Avatar
    Science Advisor

    Re: Functions.

    Is there a range for these numbers, i.e., is x any real number, integer, subset of these

    or other?
     
  6. Aug 31, 2012 #5
    Re: Functions.


    http://img214.imageshack.us/img214/5270/35240583.jpg [Broken]
    2.https://www.physicsforums.com/showthread.php?t=632495
    http://img850.imageshack.us/img850/1995/68878748.jpg [Broken]
     
    Last edited by a moderator: May 6, 2017
  7. Sep 1, 2012 #6

    Bacle2

    User Avatar
    Science Advisor

    Re: Functions.

    Well, the reason I was asking is that , if the minimum of these numbers is done

    over different subsets of the line, then the results will be different. The solution

    is straightforward: compare the functions and see which of the three dominates

    over which part of the domain, and construct a piecewise function: set

    f1>f2 ,f1>f3 , f2>f3 , etc., and select, for each interval the smallest.
     
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