What Is the Maximum Value of r(n-r) for Composite Functions?

[vkash]

Homework Statement

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

Homework Equations

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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.

 

[vela]

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.