7. Suppose that a E R, that I is an open interval containing a, that f,g :...
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7. Suppose that a E R, that I is an open interval containing
a, that f,g : 1---+ R, and that f is continuous at a.
(a) Prove that g is continuous at a if and only if f + g is continuous at a.
(b) Make and prove an analogous statement for the product fg. Show by example that the hypothesis about f you added cannot be dropped.
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