JEE Main 2016MathematicsFunctionsMediumMCQ

JEE Main 2016 — Functions Question with Solution

JEE Main 2016 (09 Apr Online)

Question

For x ∈R, x≠0, x≠1, let f0x=11-x and fn+1x=f0fnx, n=0, 1, 2,….. Then the value of f1003+f123+f232 is equal to :

Choose an option

Show full solutionCorrect option: C
Correct answer
C53

Step-by-step explanation

f1x=f0+1x=f0f0x=11-11-x=x-1x

f2x=f1+1x=f0f1x=11-x-1x=x

f3x=f2+1x=f0f2x=f0x=11-x

f4x=f3+1x=f0f3x=x-1x

∴ f0=f3=f6=…=11-x

f1=f4=f7=…=x-1x

f2=f5=f8=…=x

f1003=3-13=23 ,

f123=23-123= -12

f232=32

∴ f1003+f123+f232=53

Practice this on the real CBT interface

Solve this JEE Main question (and the rest of the Functions chapter) on PrepSharp's TCS iON-style CBT player — with timer, bookmarks and session analytics.

Solve interactively →

About this question

This is a previous-year question from JEE Main 2016, covering the Functions chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.