The value of natural number 'a' for whic...

The value of natural number 'a' for which `sum_(k=1)^(n)f(a+k)=16(2^(n)-1)`, where the function satisfies the relation `f(x+y)=f(x).f(y)` for all natural numbers x, y and further `f(1)=2` is

A

3

B

0

C

2

D

1

Verified by Experts

The correct Answer is:

A

Similar Questions

Explore conceptually related problems

If f(x) satisfies the relation f(x+ y) = f ( x) + f( y ) for all x, y in R and f(1) = 5 then

If the functions f satisfies the relation f(x+ y ) +f( x-y) = 2f ( x) f(y) AA x, yin R and f (0) ne 0 , then

Let f be a function such that f(xy)=(f(x))/y for all positive real numbers x, y. If f(20) = 15, then f(50) =

If satisfies the relation f(x+y)+f(x-y)=2 " " f(x).f(y) AA x , y in R and f(0) != 0 , then f(10)-f(-10)=

y = f(x) , Where f satisfies the relation f(x + y) = 2f(x) + xf(y) + ysqrt(f(x)) AA x, y in R and f'(0) = 0 . Then f(6) is equal to ………

Let f be a non zero continuous function satisfying f(x+y)=f(x) f(y) for all x, y in R . If f(2)=9 then f(3) is

The function 'f' satisfies the functional equation 3f(x)+2f((x+59)/(x-1))=10x+30 for all real x != 1 , then the value of f(7) is

The number of linear functions of f satisfying f(x+f(x))=x+f(x) for all x in R is