For each of the following statements, determine whether it is true or false and

Question

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

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