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Composite function of a piecewise function

  1. Jan 16, 2014 #1
    1. The problem statement, all variables and given/known data

    Given that I have a doubling function :
    f(x)=2x (for 0≤x<0.5) and 2x-1 (for 0.5≤ x<1)

    2. Relevant equations
    What is f(f(x))?


    3. The attempt at a solution
    f(f(x))=4x for the first one and 4x-3 for the second part but not sure what to do about the domain constraints...

    Thanks!!
     
  2. jcsd
  3. Jan 16, 2014 #2

    SammyS

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    It's not that simple.

    Yes, f(f(x)) = 4x over part of the domain of the composite function and 4x-3 over some other portion, but those are not the only two pieces of f(f(x)).


    For what values of x is 0 ≤ 2x < 0.5 ?

    For what values of x is 0.5 ≤ 2x < 1 ?

    etc.
     
  4. Jan 17, 2014 #3
    right, that's exactly my issue, since i don't have the fcns for 1/4 ≤ x < 1/2
    and 1/2 ≤ x < 3/4 ... is there a certain method for doing this?
     
  5. Jan 17, 2014 #4

    HallsofIvy

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    You understand that "[itex]1/4\le x< 1/2[/itex]" is part of the interval [itex]0\le x< 1/2[/itex] don't you?

    If [itex]0\le x< 1/4[/itex], f(x)= 2x which is less than 1/2 so ff(x)= f(2x)= 2(2x)= 4x.
    If [itex]1/4\le x< 1/2[/itex] then x is still between 0 and 1/2 so f(x)= 2x but f(x) is now between 1/2 and 1 so ff(x)= f(2x)= 2(2x)- 1= 4x- 1.

    Do similarly for [itex]1/2\le x< 3/4[/itex]. Now x is between 1/2 and 1 so f(x)= 2x- 1 which is between 0 and 1/2.

    If x is between 3/4 and 1, f(x)= 2x- 1 is between 1/2 and 1
     
  6. Jan 18, 2014 #5
    I understand the breakdown of the x domains, but how do you know where f(x) falls?
     
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