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-   -   Proving you have all functions and find Domain of each. (https://www.askmehelpdesk.com/showthread.php?t=328262)

  • Mar 12, 2009, 08:22 AM
    EEMILY33
    Proving you have all functions and find Domain of each.
    Cosider the functions f and g defined as follows.
    f(x) = x-3/x-2 for all x E R, does not equal 2.
    g(x) = 3-x for all x E R.
    Find all possible functions that are generated by composing the functions f and g. After finding all functions, prove that you have them all and identify the domain of each. You will want to look at (f of g), g of f, f of f, g of g, f of(g of f) and so on.
  • Mar 12, 2009, 08:25 AM
    Curlyben
    Thank you for taking the time to copy your homework to AMHD.
    Please refer to this announcement: Ask Me Help Desk - Announcements in Forum : Homework Help
  • Mar 13, 2009, 03:45 PM
    galactus
    Composing functions just means you sub one function into the other.

    For instance, f of g. Plug g in for x in f.





    Now, you try the others and let's see what you get.

    The domain of the first and last ones is everything except 1, because x=1 will result in division by 0.
  • Mar 13, 2009, 03:47 PM
    Askmeexperrt21
    Is this even logical?
  • Mar 13, 2009, 03:56 PM
    galactus
    What do you mean, is it logical? They are just composite functions.

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