A Show The Absolute Value Function Fx X

(a) Show that the absolute value function F(x) = |x| is continuous everywhere.
(b) Prove that if f is a continuous function on an interval, then so is | f |.
(c) Is the converse of the statement in part (b) also true? In other words, if | f | is continuous, does it follow that f is continuous? If so, prove it. If not, find a counterexample.

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