I am completely lost for the following question. Can someone help?

If http://data.artofproblemsolving.com/...4c16f1baa6.gif is continuous and A is a bounded subset of http://data.artofproblemsolving.com/...6c599776c2.gif, prove that http://data.artofproblemsolving.com/...51a3384683.gif. Is this necessarily true if A is not bounded?