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 

Most Viewed Questions

Preparation Products

Knockout CUET (Physics, Chemistry and Mathematics)

Complete Study Material based on Class 12th Syllabus, 10000+ Question Bank, Unlimited Chapter-Wise and Subject-Wise Mock Tests, Study Improvement Plan.

₹ 7999/- ₹ 4999/-
Buy Now
Knockout CUET (Physics, Chemistry and Biology)

Complete Study Material based on Class 12th Syllabus, 10000+ Question Bank, Unlimited Chapter-Wise and Subject-Wise Mock Tests, Study Improvement Plan.

₹ 7999/- ₹ 4999/-
Buy Now
Knockout JEE Main (Six Month Subscription)

- AI Coach Study Modules, - Unlimited Mock Tests, - Study Improvement Plan.

₹ 9999/- ₹ 8499/-
Buy Now
Knockout JEE Main (Nine Month Subscription)

- AI Coach Study Modules, - Unlimited Mock Tests, - Study Improvement Plan.

₹ 13999/- ₹ 12499/-
Buy Now
Knockout NEET (Six Month Subscription)

- AI Coach Study Modules, - Unlimited Mock Tests, - Study Improvement Plan.

₹ 9999/- ₹ 8499/-
Buy Now
Boost your Preparation for JEE Main with our Foundation Course
 
Exams
Articles
Questions