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

Find the natural number a for which sum_(k=1)^nf(a+k)=16(2^n-1), where the function f satisfies the relation f(x+y)=f(x)f(y) for all natural number x , ya n d ,fu r t h e r ,f(1)=2.

if f: 9R to 9R satisfies f(x+y)=f(x)+f(y) , for all x, y , in 9 R and f(1)=10 then sum_(r=1)^(n) f(r)

Let f be a function satisfying f(x+y)=f(x) + f(y) for all x,y in R . If f (1)= k then f(n), n in N is equal to

If a function satisfies (x-y)f(x+y)-(x+y)f(x-y)=2(x^2 y-y^3) AA x, y in R and f(1)=2, then

If a function satisfies f(x+1)+f(x-1)=sqrt(2)f(x) , then period of f(x) can be

Let f be differentiable function satisfying f((x)/(y))=f(x) - f(y)"for all" x, y gt 0 . If f'(1) = 1, then f(x) is

If 2f(x)=f(x y)+f(x/y) for all positive values of x and y,f(1)=0 and f'(1)=1, then f(e) is.

If f: R rarrR satisfying: f(x-f(y)) = f(f(y) +f(x)-1, for all x, y in R , then -f(10) equals.

For x inR - {1} , the function f(x ) satisfies f(x) + 2f(1/(1-x))=x . Find f(2) .

If for all x,y the function f is defined by f(x)+f(y)+f(x).f(y)=1 and f(x)gt0. Then show f'(x)=0