JEE Main 2022MathematicsFunctionsHardMCQ

JEE Main 2022 — Functions Question with Solution

JEE Main 2022 (26 Jul Shift 1)

Question

Let f:R→R be a continuous function such that f3x-fx=x. If f8=7, then f14 is equal to:

Choose an option

Show full solutionCorrect option: B
Correct answer
B10

Step-by-step explanation

Given f3x-fx=x

Now replance x by x3  infinite times,

fx-fx3=x3

fx3-fx32=x32..

On adding, we get

fx-limn→∞fx3n=x13+132+⋯+∞

fx-limn→∞fx3n=x131-13=x2

⇒  fx-f0=x2

Given f8=7

so f8-f0=4

i.e. f0=3

∴  fx=x2+3

Hence f14=10

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About this question

This is a previous-year question from JEE Main 2022, 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.