Let $f: \mathbb{R} \to \mathbb{R}$ and $\exists \ \ b \in \mathbb{R} : f(x+b)=\sqrt{f(x)-f^2(x)}+\frac{1}{2}$
Periodicity of a Function Given the Functional Equation $f(x+a)=\frac12+\sqrt{f(x)-\big(f(x)\big)^2}$