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f(x)=αxx+1 \large f(x) = \frac{\alpha x}{x+1} f(x)=x+1αx
For x≠−1x\ne-1x=−1, consider a function fff as described above for some constant α\alphaα. What is the value of α \alphaα for which f(f(x))f(f(x)) f(f(x)) is an identity function?
Clarification: g(x)g(x) g(x) is an identity function if g(x)=xg(x) = xg(x)=x.
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