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Understand the Properties of Functions

  1. May 14, 2013 #1
    1. The problem statement, all variables and given/known data

    Given f(x) = 1-x
    Show that 2f(3x + 1) = -6x

    2. Relevant equations



    3. The attempt at a solution
    I've tried many approaches, but I seem to be missing something. The latest approach was as follows and did not work.

    Divide by 2.
    f(3x + 1) = -3x
    f(3x) + f(1) = -3x
    3f(x) + f(1) = -3x
    3(1-x) + 0 = -3x
    3 - 3x = -3x
    3 = 0 which is obviously not true.

    Can anyone help me out with this?
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. May 14, 2013 #2

    Dick

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    Science Advisor
    Homework Helper

    You are going about this completely the wrong way and using properties of f that aren't even true. To find f(3x+1) just substitute (3x+1) for x in 1-x. Doesn't that make more sense?
     
  4. May 14, 2013 #3
    ##2f(3x+1)=2(1-(3x+1))=2(-3x)=-6x##.

    Think of it this way: If ##f(x)=1-x##, then ##f(Lemon \, cake) = 1 - (Lemon \, cake)##, in the unlikely event that the quantity 1-(Lemon cake) is defined.
     
  5. May 14, 2013 #4
    I was over-thinking it. Thank you!
     
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