# What's the period?

Calculus Level pending

Suppose a function $$f: \mathbb{R} \to \mathbb{R}$$ has the satisfies $$f(x+a) = \frac{1}{2} + \sqrt{ f(x) - (f(x))^2 }$$ for all $$x.$$

If the period of $$f(x)$$ is $$n \times a$$, then find $$n.$$

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