Question: are odd functions one to one?
Answer: A one-to-one function is a function f such that f(a) = f(b) implies a = b. Not all odd functions are one-to-one. ... It is an odd function, because, for all x in the domain of f, -f(x) = f(-x) = 0. However, it is not a one-to-one function because f(a) = f(b) = 0 does not imply a = b, unless the domain contains only zero.