Let , where the function satisfies for all natural numbers and . Then the natural…

MATHEMATICS · Single correct · CBSE · Mathematics · Relations and Functions · Relations and Functions

Problem

Let

\sum_{k=1}^{10} f(a+k) = 16(2^{10}-1)

, 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: (a) 2 (b) 16 (c) 4 (d) 3