1. Not finding help here? Sign up for a free 30min 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!

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

    vela

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    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.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook