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Let S be the set R∖{0,1}. Define functions from S to S by ϵ(x)=x, f(x)=1/(1−x), g(x)=(x−1)/x....

Let S be the set R∖{0,1}. Define functions from S to S by
ϵ(x)=x, f(x)=1/(1−x), g(x)=(x−1)/x.

Show that the collection {ϵ,f,g} generates a group under composition and compute the group operation table.

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