if f(f(X))=81. then. value of x=?
when f(X)=2X-1+f(X-1). is not equal to zero and f(X=0)=0

• f(X=0) = 0
  
  f(X=1) = 2*1-1+f(1-1)
  = 2-1+0
  = 1
  
  f(X=2) = 2*2-1+f(2-1)
  = 4-1+1
  = 4
  
  f(X=3) = 2*3-1+f(3-1)
  = 6-1+4
  = 9
  
  ===>f(X=n) = n^2
  f(f(X)) = 81
  X = sqrt(sqrt(81)) = 3
  
• 10 years agoHelpfull: Yes(32) No(0)
• f(X=0) = 0
  
  f(X=1) = 2*1-1+f(1-1)
  = 2-1+0
  = 1
  
  f(X=2) = 2*2-1+f(2-1)
  = 4-1+1
  = 4
  
  f(X=3) = 2*3-1+f(3-1)
  = 6-1+4
  = 9
  
  ===>f(X=n) = n^2
  f(f(X)) = f(f(x=3)) = f(x=9)=9^2=81 [ i.e, f(x=3)=3^2=9]
  
  so ans is x=3.
  
• 10 years agoHelpfull: Yes(6) No(0)
• f(f(X))=81
  X=3
• 10 years agoHelpfull: Yes(2) No(3)
• x=9, we find f(1)=1,f(2)=4,f(3)=9,f(4)=16... so f(9)=81.
• 10 years agoHelpfull: Yes(2) No(2)
• f(f(x))=81
  
  f(x)*f(x)=81
  9*9=81 //only possible value for f(x)=9
  
  it's means f(x)=9 not for x=9
  so, let we go to find what of x=f(x)=9
  
  in problem f(x)=2x-1+f(x-1) and f(x=0)=0
  
  so put x=1 in f(x)
  we find
  f(X=1) = 2*1-1+f(1-1) means
  f(1)=2*1-1+f(1-1)
  = 2-1+f(0) //f(0)=0 according to question
  =2-1+0
  = 1
  
  and now put 2 in f(x)
  f(X=2) = 2*2-1+f(2-1)
  = 4-1+f(1) //we already find f(1) that is 1 so we simply put f(1) value
  = 4-1+1
  =4
  
  now we put x=3 in f(x)
  f(X=3) = 2*3-1+f(3-1)
  f(3)=2*3-1+f(3-1)
  = 6-1+f(2) //we already find f(2)=4 not f(3-1)=2
  = 6-1+4
  =9
  
  so, x=3 that is put in f(x) that gives f(3)=9
  
  f(x)*f(x)=81
  f(3)*f(3)=81
  9*9=81
  
  X=3 Ans
• 7 years agoHelpfull: Yes(1) No(0)
• function=81 x=3
• 10 years agoHelpfull: Yes(0) No(0)