JEE Main 2016 — Functions Question with Solution
From: JEE Main 2016 (Online) 9th April Morning Slot
Question
For x R, x 0, Let f0(x) = and
fn+1 (x) = f0(fn(x)), n = 0, 1, 2, . . . .
Then the value of f100(3) + f1 + f2 is equal to :
fn+1 (x) = f0(fn(x)), n = 0, 1, 2, . . . .
Then the value of f100(3) + f1 + f2 is equal to :
Choose an option
Show full solutionCorrect option: B
Correct answer
B
Step-by-step explanation
As fn+1(x) = f0(fn(x))
f1(x) = f0+1(x) = f0(f0(x)) = =
f2(x) = f1+1(x) = f0(f1(x)) = = x
f3(x) = f2+1(x) = f0(f2(x)) =
f4(x) = f3+1(x) = f0(f3(x)) = =
f0(x) = f3(x) = f6(x) = . . . . . =
f1(x) = f4(x) = f7(x) = . . . . . .=
f2(x) = f5(x) = f8(x) = . . . . . . = x
So, f100(3) = =
f1 = =
f2 =
f100(3) + f1 + f2
= +
=
f1(x) = f0+1(x) = f0(f0(x)) = =
f2(x) = f1+1(x) = f0(f1(x)) = = x
f3(x) = f2+1(x) = f0(f2(x)) =
f4(x) = f3+1(x) = f0(f3(x)) = =
f0(x) = f3(x) = f6(x) = . . . . . =
f1(x) = f4(x) = f7(x) = . . . . . .=
f2(x) = f5(x) = f8(x) = . . . . . . = x
So, f100(3) = =
f1 = =
f2 =
f100(3) + f1 + f2
= +
=
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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.