JEE Main 2020 — Functions Question with Solution
From: JEE Main 2020 (Online) 6th September Evening Slot
Question
Suppose that a function f : R R satisfies
f(x + y) = f(x)f(y) for all x, y R and f(1) = 3.
If then n is equal to ________ .
f(x + y) = f(x)f(y) for all x, y R and f(1) = 3.
If then n is equal to ________ .
Enter your answer
Show full solutionCorrect answer: 5
Correct answer
5
Step-by-step explanation
f(x + y) = f(x) f(y)
put x = y = 1
f(2) = (ƒ(1))2 = 32
put x = 2, y = 1
f(3) = (ƒ(1))3 = 33
Similarly f(x) = 3x
f(i) = 3i
Given,
3 + 32 + 33 +.... + 3n = 363
= 363
3n - 1 = = 242
3n = 243 = 35
n = 5
put x = y = 1
f(2) = (ƒ(1))2 = 32
put x = 2, y = 1
f(3) = (ƒ(1))3 = 33
Similarly f(x) = 3x
f(i) = 3i
Given,
3 + 32 + 33 +.... + 3n = 363
= 363
3n - 1 = = 242
3n = 243 = 35
n = 5
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