Which of the following functions is the inverse of itself?
A function is its own inverse if \(f(f(x)) = x\).
For \(f(x) = \frac{1-x}{1+x}\): \(f(f(x)) = \frac{1 - \frac{1-x}{1+x}}{1 + \frac{1-x}{1+x}} = \frac{(1+x) - (1-x)}{(1+x) + (1-x)} = \frac{2x}{2} = x\)
So it is its own inverse.
Answer: (A)
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