Can the following equation be rewritten as a function, $f(F(x))$, of $F(x)$? I.e. as $y = f(F(x))$?
\begin{equation} F(x) = - x \log_2 x - (1-x) \log_2 (1-x) \end{equation}
where $x = (1+\sqrt{1-y^2})/2$ and $y$ takes values between $0$ and $1$.
I'm thinking the answer is no, but hopefully it's yes!