Question

Let Σf(a k) = 16(2¹⁰ – 1) x ∈ [k = 1, 10] where the function f satisfies f(x + y) = f(x)f(y) for all natural numbers x, y and f(1) = 2. Then the natural number ‘a’ is :

(1) 2  (2) 3  (3) 16  (4) 4

Answer 1

Correct option (2) 3 

Explanation:

Given f(1) = 2 and f(x + y) = f(x) . f(y)

at x = 1, y = 1 ⇒ f(2) = f(1) . f(1) = 2²

x = 2, y = 1 ⇒ f(3) = f(2) . f(1) = 2³