1) Let f: D-->R and define |f|: D-->R by |f|(x)=|f(x)|. Suppose that f is continuous at c elements of D. Prove that |f| is continuous at c.

2) If |f| is continuous at c, does it follow that f is continuous at c? Justify your answer.

----I don't know where to start for 1) but for 2), I would think that f is continuous at c since it is part of |f|. Is this proper logic?

Thanks.