Let f0(x)=1/1-x and f n+1 (x)=f 0(f n(x)), n=0,1,2,3,..... then the value of f 100(3) + f 1(2/3) + f2 (3/2) is equals to :

Answers (1)

Solution:    We have ,  

                f_0(x)=frac11-x

       Rightarrow        f_1(x)=f_0(f_0(x))=f_0(frac11-x)=frac11-frac11-x

       Rightarrow                              f_1(x)=fracx-1x

      Rightarrow        f_2(x)=f_0(f_1(x))=f_0(fracx-1x)=x

      Similarly      f_3(x)=frac11-x,f_4(x)=x ..................,f_100(x)=fracx-1x

      	herefore              f_100(3)+f_1(frac23)+f_2(frac32)=frac3-13+fracfrac23-1frac23+frac32=frac53 

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