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## Main Question or Discussion Point

trying to learn how to do proofs. So I have A=> B which is injective and E [itex]\subseteq[/itex] B then prove f^-1(f(E)) = E.

So let x [itex]\in[/itex] f^-1(f(E)) => thus f(x) [itex]\in[/itex] f(E) => x[itex]\in[/itex] E

So I have proved that x is a point within E, a subset of A, to me I think I am missing something and have not proved f^-1(f(E)) = E.

any suggestions?

So let x [itex]\in[/itex] f^-1(f(E)) => thus f(x) [itex]\in[/itex] f(E) => x[itex]\in[/itex] E

So I have proved that x is a point within E, a subset of A, to me I think I am missing something and have not proved f^-1(f(E)) = E.

any suggestions?