Algebraic Illusion

Algebra Level 5

Let \(f\) be an injective function such that \[f(n)=2f(m)\] for every pair of real numbers \( (m, n) \) satisfying the equation \[ m^2+\frac{2m}{n}-1=0 \] Also, \[f(0.06258)=\frac{1}{16}\] What is the value of \( \lfloor 100f^{-1}(1) \rfloor \)?

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