FUNctional Equation

Level pending

A function \(f(x)\) satisfies the equation \(f(4x(x+1))=2(f(x))^2-1\). If \(f(0)>0\), \(f(-1)>0\), and \(f(\frac{-1}{2})<0\), what is the value of \(| f(\frac{-1}{2}) | \)?

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