Pre-Image / Image proof

I'm new to topology and have a pretty basic proof to perform but haven't had much experience with proofs and could use some help,

Question asks, to prove that if f: A -> B and X is a subset of A

prove that X is a subset of f^-1( f(X)) i.e that X is a subset of the pre-image of the image of X,

this makes perfect sense to me that it's true but i'm unsuer how to construct the proof any help would be appreciated, cheers.

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Originally Posted by monster

Question asks, to prove that if f: A -> B and X is a subset of A prove that X is a subset of f^-1( f(X)) i.e that X is a subset of the pre-image of the image of X,

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If then, . But by definition, , then, satisfies the condition for being in . As a consequence, .