Mathematics

Problem

Let

f

be a real valued function defined for all real numbers

x

such that

0 \le f(x) \le \frac{1}{2}

and

f(x+p) = \frac{1}{2} - \sqrt{f(x) - (f(x))^2}, \quad p > 0, \text{ show that } f(x) \text{ is periodic.}