Let f and g be Lipschitz functions on A. (a) Show that the sum f + g

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) 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.