f(n) is a function...where f(f(n))+f(n)=2n+3. f(0)=1;find f(2012)

• given, f(f(n)) + f(n) = 2n+3 -----(1)
  also, f(0)=1
  put n=0 in(1)
  => f(f(0))+ f(0)=2*0+3
  => f(1)+ 1 = 3
  => f(1)= 2
  
  put n=1 in (1)
  f(f(1)) + f(1) = 2*1 + 3
  => f(2) + 2 = 5
  => f(2) = 3
  
  so on
  f(3) = 4
  f(4) = 5
  ---
  ----
  
  f(2012) = 2013
• 9 years agoHelpfull: Yes(54) No(0)
• f(f(n)+ f(n)=2n+3
  put n=0 as we know f(0)=1;
  f(1)+1=3
  hence f(1)=2
  similarly f(2012)= 2013
• 9 years agoHelpfull: Yes(0) No(0)
• ANSWER==> f(2012)=2013
  given f(0)=1----
  and
  f(f(n))+f(n)=2n+3----
  now put n= 0 in equ and we get
  f(f(0))+ f(0)=2*0+3
  f(1)+ 1 = 3
  f(1)= 2
  again for f(2)=3
  f(3)=4, f(4)=5...... so f(2012)=2013
  
• 9 years agoHelpfull: Yes(0) No(0)
• ans:-2013
  
• 9 years agoHelpfull: Yes(0) No(0)