if f(f(n)) + f(n) =2n+3
and f(0)=1
f(2012)=?

• f(0)=1
  f(f(0))+f(0)=2*0+3
  f(1)+1=3-1=2
  f(f(1))+f(1)=2*1+3=5
  f(2)=5-2=3
  likewise, f(3)=4
  ....f(n)=n+1
  f(2012)=2012+1=2013
• 10 years agoHelpfull: Yes(2) No(0)
• answer is 2013
• 10 years agoHelpfull: Yes(0) No(0)
• The identity is f(f(n)) + f(n) = 2n+3 and f(0) = 1
  now,
  for n = 0,
  f(f(0)) + f(0) = 2*0 + 3 = 3,
  => f(1) + 1 = 3
  => f(1) = 2
  for n = 1,
  f(f(1)) + f(1) = 2*1 + 3 = 5
  => f(2) + 2 = 5
  => f(2) = 3
  Similarly, f(3) = 4, f(4) = 5 and so on.
  So, f(2012) = 2012 + 1 =2013.
• 9 years agoHelpfull: Yes(0) No(0)