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(2x+3)+f(2x+7)=2AAx in R , then find the fundamental period of f(x) .

If f: RvecR is a function satisfying the property f(2x+3)+f(2x+7)=2AAx in R , then find the fundamental period of f(x)dot

If f(2+x)=a+[1-(f(x)-a)^4]^(1/4) for all x in R ,then f(x) is periodic with period

If f:R rarr R is a function satisfying the equation f(3x+1)+f(3x+10)=10, Aax in R , then the period of f(x) is

The function f(x)=|cos| is periodic with period

If f is a periodic function then

If f(x) is periodic function with period, T, 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.

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