Given that \(f : x \to \frac{2x - 1}{x + 2}, x \neq -2\), find \(f^{-1}\), the inverse of f.
A. \(f^{-1} : x \to \frac{1+2x}{2-x}, x \neq 2\) B. \(f^{-1} : x \to \frac{1-2x}{x+2}, x \neq -2\) C. \(f^{-1} : x \to \frac{1-2x}{x-2}, x \neq 2\) D. \(f^{-1} : x \to \frac{1+2x}{x+2}, x \neq -2\)
