For each of the following statements, determine whether it is true or false and justify your answer. a) If the function f + g: R -> R is continuous, then the functions f: R -> R and g: R -> R also are continuous. b) If the function f^2: R -> R is continuous, then so is the function f: R -> R. c) If the functions f + g: R -> R and g: R -> R are continuous, then so is the function f: R -> R. d) Every function f: N -> R is continuous, where N denotes the set of natural numbers.
Explanation / Answer
a) If the function f + g: R -> R is continuous, then the functions f: R -> R and g: R -> R also are continuous. false if f= 1 for all x>= 1 and g =1 for all x