Need help with a subset proof

Here's the problem:

Let X and Y be sets. Let f: X --> Y, and let A be a subset of Y.
Prove that f(f^-1(A)) is a subset of A.

Any help is much appreciated!

Quote:

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Originally Posted by widenerl194

Let X and Y be sets. Let f: X --> Y, and let A be a subset of Y.
Prove that f(f^-1(A)) is a subset of A.

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Can you describe what looks like in set-theoretic terms?
If not, there is a place for you to begin,

I think it might be

f(f^-1(A)) = f(x) is an element of X such that f(x) is an element of f(A).