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Homework Help: Function Help

  1. Apr 2, 2008 #1
    1. The problem statement, all variables and given/known data

    If f{x + p } = f{x} for all x..then p is called the period of the function.

    This part is clear to me.Now the book says...

    The period of the function f{ax + b} is b/a.Can someone lead me through.

    2. Relevant equations

    N/A
     
  2. jcsd
  3. Apr 2, 2008 #2

    tiny-tim

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    Hi physixguru! :smile:

    hmm :confused: … I think they must mean:
    The period of a function f for which f{ax + b} = f{x} for all x is b/a. :smile:

    EDIT: ooh … that's not right … thinks … I think they mean the same f, and it's p not b:

    The period of f{ax + b} is p/a. :smile:

    Hint: put g(x) = f(ax + b). Then … ? :smile:
     
    Last edited: Apr 2, 2008
  4. Apr 2, 2008 #3
    I need the xplanation.
     
  5. Apr 2, 2008 #4

    tiny-tim

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    Hi! see edit of previous post.

     
  6. Apr 2, 2008 #5

    HallsofIvy

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    If f is a function with period p, that is, if f(x+ p)= f(x) for all x, then f completes one period as x goes from 0 to p. g(x)= f(ax+ b) will complete a period as ax+ b goes from 0 to p. That is, from ax+ b= 0 so x= -b/a, to ax+ b= p so x= (p- b)/a that is a "distance" of (p- b)/a- (-b/a)= p/a- b/a+ b/a. If f has period p, then f(ax+ b) has period p/a, not b/a.
     
  7. Apr 4, 2008 #6
    Thats right...i was cured when ya told me that it was p/a.
    thnx all.
     
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