JEE Main 2021 — Functions Question with Solution
From: JEE Main 2021 (Online) 31st August Evening Shift
Question
Let f : N N be a function such that f(m + n) = f(m) + f(n) for every m, nN. If f(6) = 18, then f(2) . f(3) is equal to :
Choose an option
Show full solutionCorrect option: B
Correct answer
B54
Step-by-step explanation
f(m + n) = f(m) + f(n)
Put m = 1, n = 1
f(2) = 2f(1)
Put m = 2, n = 1
f(3) = f(2) + f(1) = 3f(1)
Put m = 3, n = 3
f(6) = 2f(3) f(3) = 9
f(1) = 3, f(2) = 6
f(2) . f(3) = 6 9 = 54
Put m = 1, n = 1
f(2) = 2f(1)
Put m = 2, n = 1
f(3) = f(2) + f(1) = 3f(1)
Put m = 3, n = 3
f(6) = 2f(3) f(3) = 9
f(1) = 3, f(2) = 6
f(2) . f(3) = 6 9 = 54
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This is a previous-year question from JEE Main 2021, 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.