relation function

Question

Let f: X→X such that f(f(x)) = x for all x∈X. then

 

1) f is one to one and onto

 2) f is one to one but not onto

3)f is onto but not one to one

4) f need not be either one to one or onto

 

Answer 1

1) because f is its own left and right inverse and therefore both surjective and injective.