Question: Let f and g be Lipschitz functions on A. (a) Show that the sum f + g is also a Lipschitz function on A. (b)

Let f and g be Lipschitz functions on A.
(a) Show that the sum f + g is also a Lipschitz function on A.
(b) Show that if f and g are bounded on A, then the product fg is a Lipschitz function on A.
(c) Give an example of a Lipschitz function f on [0, ∞) such that its square f2 is not a Lipschitz function.

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