Correct Answer: Option B

Explanation

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

x \(\neq\) 2

Let y = f(x) = \(\frac{1}{2 - x}\)

y = \(\frac{1}{2 - x}\)

y(2 - x) = 1

2y - xy = 1

2y - 1 = xy

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

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

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

= \(\frac{-2}{\frac{-1}{2}}\) = -2 x \(\frac{-2}{1}\) = 4

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