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Find these function!

  1. Feb 1, 2009 #1
    Find all the fumction F: R[tex]\rightarrow[/tex]R So that :
    1) f(x+y)=f(x)(a-y) + f(y)f(a-x)

    I don`t know if i posted in the right place , but if not please moderators send me an email.
  2. jcsd
  3. Feb 1, 2009 #2
    I suppose a is a given constant and first rule is for all x, y from R.

    First assume x=y=0: 1/2 = 1/2 a + 1/2 f(a) [tex]\Rightarrow[/tex] f(a) = 1-a (1)
    Then x=0 and y=a: f(a) = 1/2 . 0 + f(a)2 [tex]\Rightarrow[/tex] f(a) = 0 or 1 (2)
    f(a) can't be 1, because then according (1) a=0 and f(0) is 1/2.
    Let's assume x=a and y=0: f(a) = f(a)2 + 1/4 and f(a)=0 [tex]\Rightarrow[/tex] 0=1/4

    This function can't exist.
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