Linear Maps

  • Thread starter Kosh11
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  • #1
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Homework Statement



741xH.png


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?
 

Answers and Replies

  • #2
lanedance
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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
 
  • #3
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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?
 
  • #4
lanedance
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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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