Determine if each function is continuous at the given value of a. Justify your answers using limits and the definition of continuity. If any functions are NOT continuous at a, determine which properties of continuity are satisfied and which properties fail. (a) f(x) = x² - 4x +3/x-3 at a = 3
(b) g(x) = x² - 4x + 3 - 3 if r73 if r = 3 at a=3.
(c) For the function g(x) in part (c), how would you "remove the discontinuity"? In other words, how could you re-define g(x) in order to make it continuous at a = 3? Be sure to write your new function g(x).