Double functions?

• Zeitiax

  8 Jan 08, 19:49

  Can anyone help me in solving this question..
  
  f(x) = f(x/2002) + 3x
  Find f(2)
  
  And what topic does this kind of question falls under?
  
  Thanks in advance.
• eagle

  8 Jan 08, 19:55

  Originally posted by Zeitiax:

  Can anyone help me in solving this question..
  
  f(x) = f(x/2002) + 3x
  Find f(2)
  
  And what topic does this kind of question falls under?
  
  Thanks in advance.

  Glad your first post was made in Homework Forum
  
  First, if you could not solve such questions or cannot see where it is going, you could actually try to write it out like the following
  
  f(2) = f(2/2002) + 3 (2)
  f(2/2002) = f(2/2002^2) + 3 (2/2002)
  f(2/2004) = f(2/2002^3) + 3 (2/2002^2)
  and so on
  
  You will find that it will end up something similar to
  
  3(2) + 3 (2/2002) + 3 (2/2002^2) + ....
  
  Similar to a GP
  first term 6
  rth term 1/2002
  and Sum to Infinity
  
  Thus,
  f(2) = a / (1 - r) = 6.003
• Zeitiax

  8 Jan 08, 20:00

  That was fast, hope i get a clue about what's happening after i read your post a few more times.. looks... complicated.. hmm...
• eagle

  8 Jan 08, 20:01

  Originally posted by Zeitiax:

  That was fast, hope i get a clue about what's happening after i read your post a few more times.. looks... complicated.. hmm...

  write it out. You will understand better
• Zeitiax

  8 Jan 08, 20:08

  So basically its just continuing the pattern until its is sufficient? ( In this case, to 3 dec. places )
• eagle

  8 Jan 08, 21:09

  Originally posted by Zeitiax:

  So basically its just continuing the pattern until its is sufficient? ( In this case, to 3 dec. places )

  More of continuing till you see the pattern
• Zeitiax

  8 Jan 08, 21:56

  What does a and r represent?
  
  I'm still quite new to series... so... having some problem. hehe..
  
  EDIT:
  
  Found what they represent,
  
  anyway, I've got the question wrong, no wonder the answer looks weird,
  
  f(x) = f(2002/x) + 3x
  Find f(2)
  
  It should be the other way.. and some how... I don't know how to apply the sum to infinity of a G.P., is it because its no longer a G.P.?
• eagle

  8 Jan 08, 22:24

  Originally posted by Zeitiax:

  What does a and r represent?
  
  I'm still quite new to series... so... having some problem. hehe..
  
  EDIT:
  
  Found what they represent,
  
  anyway, I've got the question wrong, no wonder the answer looks weird,
  
  f(x) = f(2002/x) + 3x
  Find f(2)
  
  It should be the other way.. and some how... I don't know how to apply the sum to infinity of a G.P., is it because its no longer a G.P.?

  I think the question like this more wrong:
  
  f(2) = f(2002/2) + 3(2)
  f(2002/2) = f(2) + 3(1001)
  
  f(2) = f(2) + 3 (1001) + 3 (2)
  0 = 3 (1003) ?????
  
  
• Zeitiax

  8 Jan 08, 22:30

  lol... Didn't notice that.. maybe i'll check the question with my friend again.
  
  Thanks for your help and time..