Let `f(x)` be periodic and `k` be a positive real number such that `f(x+k)+f(x)=0fora l lx in Rdot` Prove that `f(x)` is periodic with period `2kdot`

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

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

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

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

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

If f: Rrarr[0,oo) is a function such that f(x-1)+f(x+1)=sqrt(3)f(x), then prove that f(x) is periodic and find its 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.

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 a,b are two positive numbers 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?

Prove that f(x)=x-[x] is periodic function. Also, find its period.