Consider function `f` satisfying `f(x+4)+f(x-4)=f(x)` for all real `x` .Then `f(x)` is periodic with period

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.

The function f(x)=x-[x] is a periodic with period.

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

If f:R rarr R is a function satisfying the property f(x+1)+f(x+3)=2 for all x in R than fis (1) periodic with period 3(2) periodic with period 4(3) non periodic (4) periodic with period 5

If a function satisfies f'(x)=f(x) ,then f(x)=

If f is a function of real variable x satisfying f(x+4)-f(x+2)+f(x)=0 , then f is periodic function with period:

Let f (x) be a function satisfying f (x) f (y) = f (xy) for all real x, y. If f (2) = 4, then what is the value of f((1)/(2)) ?

If f(x) satisfies the relation f(x)+f(x+4)=f(x+2)+f(x+6) for all x, then prove that f(x) is periodic and find its period.

If f(x+10) + f(x+4), there f(x) is a periodic function with period