Thread: more continuity of functions

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.

if f is continuous at c then with .
Using the same , we have
, so is continuous at c.

For 2) take a function which is -1 on and 1 on . Then is 1 and continous, but f certainly isn't.