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JEE Main20206 Sep 2020Evening ShiftMathematicsFunctionsActual

Suppose that a function f : R → R satisfies f x + y = f x f y for all x , y ε R and f 1 = 3 . If ∑ i = 1 n f i = 363 , then n is equal to ..... .

Correct answer

0

Step-by-step solution

f x = a x ⇒ f 1 = a = 3 so f x = 3 x ∑ i = 1 n f i = 363 ⇒   3 + 3 2 + . . . . . 3 n = 363 3 3 n - 1 2 = 363 3 n = 243   ⇒   n = 5

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