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QJEEM21Maeab1: JEE Main 2021 Mathematics - Class 11 JEEM21Maeab1 Solution: Let f : N N be a function such that f(m + n) = f(m) + f(n) for…
Let f : N N be a function such that f(m + n) = f(m) + f(n) for every m, n N. If f(6) = 18, then f(2) . f(3) is equal to :
Multiple Choice Options
- A 6
- B 54
- C 18
- D 36
Step-by-Step Verified Solution
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