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Let f(x) = (alpha*x)/(x + 1) for x not equal to -1. For what value of alpha does f(f(x)) = x hold for all valid x?

1. sqrt(2)
2. -sqrt(2)
3. 1
4. -1

Correct answer: -1

Solution

An involution f(f(x)) = x forces the coefficient relationships in the composed rational expression to match the identity function. This determines alpha = -1.

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