# Math Help - Proofs. Need help proving the following

1. ## Proofs. Need help proving the following

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!

2. ## Re: Proofs. Need help proving the following

Originally Posted by duckyone
[COLOR=#373737][FONT=Lucida Grande]Can anyone prove this?If S is a subset of D(f) then S is a subset of f^(-1)(f(S))
It is hard for to read your question. But I think it means:
If $f:A\to B$ and $S\subseteq A$ then $S\subseteq f^{-1}[f(S)]~.$.

The definition gives us $t\in S$ implies $f(t)\in f(S)$.

Can you finish?