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anonymous

  • one year ago

Let A be the set of all functions with domain R and codomain [-1,1]. 1. Give 2 functions that are elements of A. 2. Let R = {(f,g) l f(0) = g(0)}. Determine if the given reflection is reflexive, symmetric, and/or transitive. Give brief explanations to go with your answers. 3. Describe in words the set given by [cosx]. (We did a problem before that defined the set [x] for a given relation R by the rule [x] = {y l (x,y) ∈ R}.)

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  1. anonymous
    • one year ago
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    since and cosine come to mind right away

  2. anonymous
    • one year ago
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    they leave so very quickly...

  3. anonymous
    • one year ago
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    Thank you for your help; I really appreciate it. I realized I switched the domain and codomain for part a when I initially tried this.

  4. anonymous
    • one year ago
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    for b, does that mean f and g are each a function where their y intercepts are equal?

  5. zepdrix
    • one year ago
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    Hmm, ya it seems that way :o

  6. anonymous
    • one year ago
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    then it would definitely be reflexive since the same function would have the same points

  7. zepdrix
    • one year ago
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    Hmm, I'm not sure if I'm missing something... because showing that it's an equivalence relation almost seems trivial. Transitive: If fRg then we need gRf. So if f(0)=g(0), then g(0)=f(0) is clearly true for any functions in A.

  8. zepdrix
    • one year ago
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    Ya reflexive seems to work out clearly as well.

  9. anonymous
    • one year ago
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    Thanks :)

  10. anonymous
    • one year ago
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    For part c, I assumed the set [cosx] just meant the range [-1,1] of the function.. Is that the way to describe that in words?

  11. zepdrix
    • one year ago
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    Hmm I dunno :d the notation is confusing lol.\[\large\rm [\color{orangered}{x}]=\{y~|~(\color{orangered}{x},y)\in R\}\]Based on the previous exercise they referred to, I guess we have something like this,\[\large\rm [\color{orangered}{\cos x}]=\{y~|~(\color{orangered}{\cos x},y)\in R\}\]So we need ... words? Like human words for this? Hmmm..

  12. zepdrix
    • one year ago
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    This is the `set of y values such that cos x is in relation to y`. That's how I would read it. So ya, it's uhhh.. the entire range right? as you said? :o

  13. zepdrix
    • one year ago
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    there's probably some pretty way to word that >.<

  14. freckles
    • one year ago
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    [cos(x)] is the set of functions f with domain all real numbers and codomain [-1,1] and cos(0)=f(0)

  15. freckles
    • one year ago
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    it has been a while since I looked at words codomain and range I think the range of the function can actually be a subset of the codomain and they used the word codomain earlier not range

  16. freckles
    • one year ago
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    so I think one element of [cos(x)] would be f(x)=1 since cos(0)=f(0)=1 that is just one example what one of the elements I think we would have

  17. freckles
    • one year ago
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    also I'm under the assumption we are using the way R was defined in 2...

  18. dan815
    • one year ago
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    also circles and ellipses

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