\(f(x) = \frac{1}{2 - x}, x \neq 2\)

\(f(y) = \frac{1}{2 - y}\)

\(x = \frac{1}{2 - y}\) (Let x = f(y))

\(2x - xy = 1 \implies y = \frac{2x - 1}{x}\)

\(\therefore f^{-1}(x) = \frac{2x - 1}{x}\)

\(f^{-1}(-\frac{1}{2}) = \frac{2(-\frac{1}{2}) - 1}{-\frac{1}{2}}\)

= \(-2 \times -2 = 4\)