Question Number 2253 by 123456 last updated on 11/Nov/15

f_n :[0,1]→[0,1],g:[0,1]→[0,1] f_(n+1) (x)=g[f_n (x)]+f_n [g(x)] f_0 (x)=x f_4 (x)=? g(x)=x^2 ,f_2 (2)=??

Commented byRasheedAhmad last updated on 12/Nov/15

Definition g(x)=x^2 only for f_2 (2) ?

Answered by prakash jain last updated on 12/Nov/15

f_1 (x)=g[f_0 (x)]+f_0 [g(x)]=g(x)+g(x)=2g(x) f_1 (x)=2x^2 f_2 (x)=g(2x^2 )+f_1 (x^2 )=4x^4 +2x^4 =6x^4 f_3 (x)=(6x^4 )^2 +6x^8 =42x^8 f_4 (x)=(42x^8 )^2 +42(x^2 )^8 =42×43x^(16)