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## Main Question or Discussion Point

Any help on this problem would be appreciated

a) Show that (f^-1 S)compliment is equal to f^-1(S compliment) for any set S of reals.

Then use part a) to show The function f is continuous iff f^-1(S) is closed for every closed set S.

a) Show that (f^-1 S)compliment is equal to f^-1(S compliment) for any set S of reals.

Then use part a) to show The function f is continuous iff f^-1(S) is closed for every closed set S.