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Solved: Discontinuous composite of continuous functions
Chapter 2, Problem 64E(choose chapter or problem)
PROBLEM 64E
Discontinuous composite of continuous functions Give an example of functions ƒ and g, both continuous at x = 0, for which the composite is discontinuous at x = 0. Does this contradict Theorem 9? Give reasons for your answer.
Questions & Answers
QUESTION:
PROBLEM 64E
Discontinuous composite of continuous functions Give an example of functions ƒ and g, both continuous at x = 0, for which the composite is discontinuous at x = 0. Does this contradict Theorem 9? Give reasons for your answer.
ANSWER:
Solution
Step 1 of 3
In this problem we have to give the examples of and
such that
and
are both continuous at
and
is discontinuous at
.
Assuming the example
and
We see the example shows that both functions are continuous at