Solving Unintuitive Homework: An Example of C ≠ f^(-1)(f(c))

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Homework Help Overview

The discussion revolves around a proof related to the relationship between a function and its inverse, specifically examining the condition where C does not equal f^(-1)(f(c)). The subject area involves concepts from set theory and functions.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore the initial intuition that C equals f^(-1)(f(c)) and question the implications of this assumption. There is a suggestion to start with small discrete sets to find a counterexample. One participant raises a question about the role of differentiability in the context of the problem.

Discussion Status

The discussion is active, with participants sharing ideas and examples. Some guidance has been offered regarding the use of simple sets to illustrate the concept, while questions about the necessity of differentiability remain open for exploration.

Contextual Notes

Participants are considering the implications of functions mapping elements from one set to another and the conditions under which the inverse function may not return the original element. There is a focus on finding specific examples to clarify these concepts.

Kosh11
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Homework Statement



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Homework Equations





The Attempt at a Solution



I don't know how to start a proof for this. Intuitively I would think think that C = f^(-1)(f(c)), which would imply that C is a subset of f^(-1)(f(c)), however that is not the case and the problem asks for an example when that is not true. Does this mean that f(C) sends all elements c of C from A to B and that f^(-1) sends all elements c of C from B to A?
 
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its good to start with small discrete sets and see if you can find a good example

how about considering A = {a,b} both mapped to the same point f(a) = f(b) = d
 
Thanks I kind of figured it out. One questions would a differentiable map be considered an example where if you have f(a) = d then then f^(-1)(f(a)) wouldn't necessarily equal a?
 
I'm not sure why you would need to consider differntiability? You;re just looking at maps between sets

the example I gave in post #2 should be sufficient...
 

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