Finding Discontinuous Composite Function f o g at x = 0

In summary, the task is to find two continuous functions, f and g, where the composite function f at g is discontinuous at x = 0. This can be achieved by having 0 in the denominator of the composite function, although it is possible for the composite to be discontinuous even if f and g are both continuous at x = 0. However, the reverse is not true and g at f cannot be discontinuous at x = 0 if both f and g are continuous at x = 0.
  • #1
Jan Hill
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0

Homework Statement


I need to find functions f and g both continuouis at x = 0 for which the composite f at g is discontinuous at x = 0



Homework Equations





The Attempt at a Solution

I thnk it is a matter of looking for a composite function that results in 0 being in the denominator so that it's undefined. Is that the only way to get this composite to be discontinuous?
 
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  • #2
and can it be that f\circ g is discontinuous at x = 0 if f and g are both continuous at x = 0 despite the fact that we know that g\circ f cannot be discontinuous at x = 0 if f and g are continuous at x= 0
 

Related to Finding Discontinuous Composite Function f o g at x = 0

1. What is a discontinuous composite function?

A discontinuous composite function is a type of mathematical function that is formed by combining two or more functions together. It is called "discontinuous" because the resulting function is not continuous at a certain point, meaning there is a break or "gap" in the graph of the function at that point.

2. How do you find the value of a discontinuous composite function at x = 0?

To find the value of a discontinuous composite function at x = 0, you need to first determine the individual functions that make up the composite function. Then, substitute x = 0 into each function and evaluate the resulting expressions. Finally, plug these values into the composite function and simplify to get the final answer.

3. Can a discontinuous composite function have a limit at x = 0?

Yes, a discontinuous composite function can have a limit at x = 0. In this case, the limit would be the same as the value of the function at x = 0. However, this is not always the case and the limit may not exist if the function has a jump or break at x = 0.

4. How can you determine if a composite function is continuous at x = 0?

A composite function is continuous at x = 0 if the individual functions that make up the composite function are also continuous at x = 0, and the limit of the composite function at x = 0 exists. If the limit does not exist or if there is a break or jump in the graph of the composite function at x = 0, then the function is discontinuous at that point.

5. What are some real-world applications of discontinuous composite functions at x = 0?

Discontinuous composite functions have various applications in different fields of science and engineering. For example, in physics, these functions can be used to model the behavior of objects that undergo sudden changes or impacts. In economics, they can be used to study the effects of external shocks or unexpected events on the market. In computer science, discontinuous composite functions are used in algorithms and coding to solve problems with multiple conditions and outcomes.

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