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Homework Help: What this question is saying.

  1. Aug 21, 2011 #1
    1. The problem statement, all variables and given/known data

    If the composite function f1(f2(f3(.......(fn)))) n times, is an increasing function and if r of fi's are decreasing function while rest are increasing, then find the maximum value of r(n-r)?

    2. Relevant equations


    3. The attempt at a solution

    How can i attempt if i don't know what is question.

    I request you to not put answer!!!!. I want that you just tell me question in easy language. I want to try it before anybody tell me it's answer. If you give example then it will easy to understand.
  2. jcsd
  3. Aug 21, 2011 #2


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    Say you have n=3 functions. If all of them are increasing, the composite function will be increasing, and you'd have r=0, so r(n-r)=0. You can also get an increasing composite function when r=2, in which case, you'd get r(n-r)=2. The other two cases will result in a decreasing composite function. So when n=3, the maximum value of r(n-r) is 2.

    The problem is asking you to do this for the general case. I'll leave it to you to figure out what combinations will result in an increasing composite function.
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