f(x)= 2(x) +1, f(f(f(f….f(n))))12 times = 81919. Then n=?

• f(x)=2(x)+1
  f(f(x))=2^2(x)+3
  =2^2(x)+(2^2-1)
  ''
  ''
  ''
  f(f(f(f....(x)))) 12 times= 2^12(x)+(2^12-1)
  given data from question
  => 819119=2^12(x)+2^12-1
  =>819120=2^12(x+1)
  =>20*2^12=2^12(x+1)
  =>x=19 answer.
• 8 years agoHelpfull: Yes(28) No(1)
• f(x)=2(x)+1
  f(n)=2n+1
  f(f(n))=2(2n+1)+1=4n+3
  f(f(f(n)))=2(4n+3)+1=8n+7
  f(f(f(f(n))))=2(8n+7)+1=16n+15
  .
  .
  .
  f(f(f(f.....f(n))))12times= 4096n+4095
  4096n+4095=81919
  n=19
• 8 years agoHelpfull: Yes(12) No(0)
• ans. n=40959
  
  firstly put x=19
  f(x)=2x=1=39.........................1 time
  f(x)=2*39+1=79.......................2 time
  f(x)=2*79+1=159...................3time
  .....................................................
  .............................................
  ................................
  ...................................................
  f(x)=2*40959+1=81919.........12 time
  
  ans is n=40959
• 8 years agoHelpfull: Yes(6) No(3)
• Given, f(x)=2(x) + 1 = 2^1(x) +1
  f(f(x))=f2(x)=2[(2(x)+1]+1= 4(x) + 2 +1 = 2^2(x) + 2 + 1
  f(f(f(x)))=f3(x)=4[2(x) + 1] + 2+ 1= 8(x) + 4+ 2 +1 = 2^3(x) + 4 + 2 + 1
  .
  .
  f12(x)= 2^12(n) + ( 2^12 + 2^11 + 2^10 + ................ + 2^3 + 2^2 + 2^1 + 1) ---> in Gp
  f12(x)=4096(n) + [ (2^12 - 1)/(2 - 1)]
  since f12(x) =81919
  hence,
  4096(n) + 4096 -1=81919
  after simplify...
  n=19
• 8 years agoHelpfull: Yes(3) No(0)
• 19,
  
  simulate the function for three times and you will have an expression equate it with the value and the answer is out.
  
  in this question 2^t*(n+1)=81920(i.e val+1)
• 8 years agoHelpfull: Yes(2) No(1)
• First time: (81919-1)/2=40959
  Second time: (40959-1)/2=20479
  .
  .
  Twelfth time: (39-1)/2=19
  Thus answer is 19
• 8 years agoHelpfull: Yes(1) No(0)