A function f is said to be one-to-one, or injective, iff f(a) = f(b) implies that a=b for all a and b in the domain of f.
A function f from A to B in called onto, or surjective, iff for every element b B there is an element a A with f(a)=b.
Bijective means it's both injective and surjective.
With the iff you have to be able to prove it both ways.
I'm a little confused with the total function but I think it means that every element in the domain is defined on the function.
Hope this helps