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) + g(x) are continuous at 0. (b) A function f(x) continuous at 0 and g(x) not continuous at 0 such that f(x) + 9(2) is continuous at 0. (c) A function f(2) continuous at 0 and g() 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(x) + Fle) is continuous at 0. (e) A function f(x) not continuous at O such that (f (x)]® is continuous at 0