Provide an example of each or explain why the request is impossible. (a) Two functions f and g, neither of which is continuous at 0 but such that f(x)g(x) and f(x) +9(2) are continuous at 0.
(b) A function f(x) continuous at 0 and g(2) not continuous at 0 such that f(2) + g(x) is continuous at 0.
(c) A function f(x) continuous at 0 and g(2) not continuous at 0 such that f(x)g(x) is continuous at 0.
(d) A function f(x) not continuous at 0 such that f(2) + the is continuous at 0.
(e) A function f(x) not continuous at 0 such that [f(x)]^3 is continuous at 0.