Whenever you get stuck on a problem like this the first (really important) step is to make sure you understand all of the notation/definitions being used in the question. Break it into all of its separate parts and make sure you know every piece individually before worrying about the whole. Do you indeed know what Dom(f) and surjective are, for example?
Anyway, when defining a function:
f:A→BWe say f maps elements of the set A (known as the domain / dom(f)) onto elements of the set B (known as the codomain / cod(f)).
Now, f is surjective if for every element
b∈B there exists
a∈A such that
f(a)=b, i.e. every element of B can be "reached" from some element of A.
Additionally, Im(f) is the subset of elements of B which can be reached from A.
So, if we replace B with Im(f), and consider only the elements of B which can be reached from A, we suddenly notice (unsurprisingly) that every element of the new B (Im(f)) can now be reached from A. Therefore
f:Dom(f)→Im(f) is automatically surjective.