Adjusted Composition

Algebra Level 3

\[ \large f(x) = \frac{\alpha x}{x+1} \]

For \(x\ne-1\), consider a function \(f\) as described above for some constant \(\alpha\). What is the value of \( \alpha\) for which \(f(f(x)) \) is an identity function?

Clarification: \(g(x) \) is an identity function if \(g(x) = x\).

Image Credit: Flickr Eliana Lúcio.
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