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Homework Help: Compostion of functions

  1. Nov 18, 2012 #1
    1. The problem statement, all variables and given/known data

    Let g : A → B and f : B → C where A = {a,b,c,d}, B = {1,2,3}, C = {2,3,6,8}, and g and f are defined by g = {(a,2),(b,1),(c,3),(d,2)} and f = {(1,8),(2,3),(3,2)}.

    Find f o f

    2. Relevant equations

    3. The attempt at a solution

    I know how to find f o g by working from g to f, but I'm not sure what to do with f o f. Does it simply map back to it self?

    Thanks for any suggestions.
  2. jcsd
  3. Nov 18, 2012 #2
    The map [itex]f\circ f[/itex] doesn't even make sense in this context. I think they made an error in the problem statement.
  4. Nov 18, 2012 #3
    Well actually it's f o f ^-1, but I just wanted help with the f o f part.
    Could you elaborate why this wouldn't make sense?
    Last edited: Nov 18, 2012
  5. Nov 18, 2012 #4


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    What is f o f(1)?
  6. Nov 18, 2012 #5
    (f o f)(1) = f(f(1)) = I want to say 8, but I don't think this is right.

    I think f(1) = 8.
  7. Nov 18, 2012 #6


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    So, you're saying f(f(1)) = f(8).

    Now to finish answering Dick's question ... What is f(8) ?
  8. Nov 18, 2012 #7
    I'm not really sure.
  9. Nov 18, 2012 #8
    Look in your table for f. Search for a couple (8,x). What is x?
  10. Nov 18, 2012 #9


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    You probably aren't sure because 8 isn't in the domain of f. Wouldn't this indicate a "doesn't make sense" response?
  11. Nov 18, 2012 #10
    Okay so we would mapping from 1 to 8, but then since 8 is not in the domain of f it doesn't work.
  12. Nov 18, 2012 #11
    Indeed. We can go from 1 to 8. But then we can't apply f anymore since we can't leave from 8.
  13. Nov 18, 2012 #12
    Okay, thanks for walking me through that.
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