Let f(x)=x/(1+x) and let g(x)=(rx)/(1-x)...

Let `f(x)=x/(1+x)` and let `g(x)=(rx)/(1-x)` , Let S be the set off all real numbers r such that `f(g(x))=g(f(x))` for infinitely many real number x. The number of elements in set S is

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