Question: are all even functions one to one?
Answer: A function f is one-to-one if for each a and b in the domain of f, if f(a) = f(b) then a = b. Hence if f is an even function and for some number a, a and -a are both in the domain of f then f(a) = f(-a) and yet a ≠ -a and hence f is not one-to-one.