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Trouble finding the Linear Functions that satisfy the given Identity

  1. Nov 16, 2009 #1
    1. The problem statement, all variables and given/known data

    Given f[f(x)] = 2x + 1 find all linear functions that satisfy this identity.
    Given f[f[f(x)]] = 2x + 1 find all linear functions that satisfy this identity.


    2. The attempt at a solution

    I have not started to attempt a solution at this because I have no idea how to do these types of problems.
     
  2. jcsd
  3. Nov 16, 2009 #2

    Mark44

    Staff: Mentor

    You're give that f(x) is a linear function, so let f(x) = ax + b.
    For the first problem, you know that f(f(x)) = 2x + 1, so f(ax + b) = 2x + 1, or a(ax + b) + b = 2x + 1. Solve for a and b. Hint: a and b are not rational numbers.

    Solve the second problem in a similar manner.
     
  4. Nov 16, 2009 #3
    Thanks a lot!

    For the first problem the answer would be:

    f(x) = √2x + (-1+√2) and
    f(x) = √2x + (-1-√2)

    right?

    I have yet to do the second one.
     
  5. Nov 16, 2009 #4

    Mark44

    Staff: Mentor

    Yes.
     
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