Question

Let f : D → R, D ⊆ R. Define |f| : D → R by |f|(x) = |f(x)| for
x ∈ D. Let c ∈ D.
(a) Show that, if f be continuous at c, then |f| is continuous at c.
(b) If |f| is continuous at c, does it follow that f is continuous at c?

4.2.7. Let f : D → R, D R. Define If! : D → R by lfl(z) = If(x)| for a) Show that, if f be continuous at c, then f is continuous at c. (b) If lfl is continuous at c, does it follow that f is continuous at c?