finding composition of functions, the set A is the set of real numbers EXCLUDING zero.

the function f is injective and defined by f(x) = 1 - 1/x  for all x in the set A

need to show that f of f of f is equal to i subscript A, not sure what is meant by i subscript A
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Therefore, f(f(f(x)))=x.

[For example, if x=2, f(2)=½, f(½)=-1, f(-1)=2. So f(f(f(2)))=2=x.]

i_A may indicate a definition of i_A. But I think it means any element of set A. So the compound function maps each element onto itself. Zero is excluded because it would generate 1/0 which is undefined.

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