Let f be a function satisfying `f(x) + f(x + 1) + f(x + 2 )+............+f(x+2015)=0 AA X in R`, then `f(x)` is periodic wit period

Let f(x) be a function satisfying f(x) + f(x+2) = 10 AA x in R , then

Statement -1: Let f(x) be a function satisfying f(x-1)+f(x+1)=sqrt(2)f(x) for all x in R . Then f(x) is periodic with period 8. Statement-2: For every natural number n there exists a periodic functions with period n.

Statement -1: Let f(x) be a function satisfying f(x-1)+f(x+1)=sqrt(2)f(x) for all x in R . Then f(x) is periodic with period 8. Statement-2: For every natural number n there exists a periodic functions with period n.

Let f be a differentiable function satisfying f'(x)=f' (-x) AA x in R. Then

Let f:R->R be a function such that f(x+y)=f(x)+f(y),AA x, y in R.

Let f:R->R be a function such that f(x+y)=f(x)+f(y),AA x, y in R.

Let f(x) be a periodic function with period 'p' satisfying f(x)+f(x+3)+f(x+6)+...+f(x+42)=cons tan t AA x in R ,then sum of digits of 'p' is

If f(x) is a real valued function such that f(x + 6) - f(x + 3) + f(x) = 0, AA x in R , then period of f(x) is

If f(x) is a real valued function such that f(x + 6) - f(x + 3) + f(x) = 0, AA x in R , then period of f(x) is