If `f(x) in [1,2]` where `x in R` and for a fixed positive real number `p`, `f(x+p)=1+sqrt(2f(x)-{f(x)}^2)` for all `x in R` then prove that `f(x)` is a periodic function

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(x) be periodic and k be a positive real number such that f(x+k) + f(x) = 0 for all x in R . Prove that f(x) is periodic with period 2k.

Let f(x) be periodic and k be a positive real number such that f(x+k)+f(x)=0 for all x in R. Prove that f(x) is periodic with period 2k .

If (x+(1)/(2))+f(x-(1)/(2))=f(x) for all x in R, then the period of f(x) is

Let f(x+p)=1+{2-3f(x)+3(f(x))^2-(f(x)^3}^(1//3), for all x in R where p>0 , then prove f(x) is periodic.

If f(x + 1/2) + f(x - 1/2) = f(x) for all x in R , then the period of f(x) is

Let f(x) be periodic and k be a positive real number such that f(x + k) + f (x) = 0 for all x in R . Then the period of f(x) is

Let f(x) be periodic and k be a positive real number such that f(x+k)+f(x)=0 for all x in R. Then the period of f(x) is

If a , b are two fixed positive integers such that f(a+x)=b+[b^3+1-3b^2f(x)+3b{f(x)}^2-{f(x)}^3]^(1/3) for all real x , then prove that f(x) is periodic and find its period.

If a , b are two fixed positive integers such that f(a+x)=b+[b^3+1-3b^2f(x)+3b{f(x)}^2-{f(x)}^3]^(1/3) for all real x , then prove that f(x) is periodic and find its period.