Let f be a function from the set Z of all integers into itself, that satisfies the condition for all m∈Z,
f(f(m))=−m. (1)
Then:
(a) f is a mutually unique mapping, i.e. a simple mapping of the set Z onto the set Z ,
(b) for all m∈Z holds that f(−m)=−f(m) ,
(c) f(m)=0 if and only if m=0 .
Prove these statements and construct an example of a mapping f that satisfies condition (1). algebrafunctional equationfunction