Y by Adventure10, ImSh95, Mango247, Mango247
Let
be a real-valued function defined for all real numbers, such that for some
we have
for all
.
Prove that
is periodic, and give an example of such a non-constant
for
.


![\[ f(x+a)={1\over2}+\sqrt{f(x)-f(x)^2} \]](http://latex.artofproblemsolving.com/1/f/7/1f74603bb9dc47c0ffd7fd7ee466eb8dbade34f7.png)

Prove that


