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.

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.

If f(2+x)=a+[1-(f(x)-a)^4]^(1/4) for all x in R ,then f(x) is 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 f:R->R is a function satisfying the property f(x+1)+f(x+3) = 2 for all x in R than fi s (1) periodic with period 3(2) periodic with period 4 (3) non periodic (4) periodic with period 5

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

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:

If f(x+10) + f(x+4)= 0 , there f(x) is a periodic function with period

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.