Question

If the change in entropy dS = dQ / T and that S=f(Q,T) prove that entropy is a state function .​

Answer 1

It is because the entropy of a system depends only on its state, just like its internal energy. Or, putting it the other way round, a given state of a system has a particular entropy.

The formula dS = dQ/T only applies to a reversible change, and such a change has only one path, or a few equivalent paths.