Can anyone prove this?If S is a subset of D(f) then S is a subset of f^(-1)(f(S))

So far I have:

Let x be an element of S

Therefore, f(x) is an element of f(s)

f inverse of f(s) = {p is an element of D(f) | f(p) is an element of f(s)}

since f(x) is an element of f(s), then x is an element of f inverse f(s)

Anything else I can add or omit?

Any help is very much appreciated!