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Math Help - Need help finding g of f

  1. #1
    kro
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    Talking {Solved} Need help finding g of f

    I don't understand how to solve this question below:
    Suppose g:A-->B and f:B-->C where A=B=C={1,2,3,4}, g={(1,4),(2,1),(3,1),(4,2)} and f={(1,3),(2,2),(3,4),(4,2)}.
    Find g of f

    Any help with this would be very much appreciated.
    Last edited by kro; July 31st 2009 at 01:38 AM.
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  2. #2
    MHF Contributor Swlabr's Avatar
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    Quote Originally Posted by kro View Post
    I don't understand how to solve this question below:
    Suppose g:A-->B and f:B-->C where A=B=C={1,2,3,4}, g={(1,4),(2,1),(3,1),(4,2)} and f={(1,3),(2,2),(3,4),(4,2)}.
    Find g of f

    Any help with this would be very much appreciated.
    Basically, here you have to follow a trail. Take 1 and see where it is mapped to, then look at 2, then 3 then 4. In g(f(x)) we apply f to x and then we apply g to the result. So, if x is 1 then f(x) is 3 and g(f(x)) is 1. Similarly, 2 is sent to 1. Thus, g \circ f = \{(1,1)(2,1)(3,a)(4,b)\} ( (g \circ f)(x) = g(f(x))). Can you see how to find a and b?
    Last edited by Swlabr; July 31st 2009 at 01:31 AM.
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  3. #3
    kro
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    Lightbulb I think I got it?

    Swlabr,
    Here's what I have so please let me know if this is correct:
    f(1)=3 so g(f(x))=1
    f(2)=2 so g(f(x))=1
    f(3)=4 so g(f(x))=2
    f(4)=2 so g(f(x))=1

    so......f of g = {(1,1),(2,1),(3,2),(4,1)}

    Is this correct?
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  4. #4
    MHF Contributor Swlabr's Avatar
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    Quote Originally Posted by kro View Post
    Swlabr,
    Here's what I have so please let me know if this is correct:
    f(1)=3 so g(f(x))=1
    f(2)=2 so g(f(x))=1
    f(3)=4 so g(f(x))=2
    f(4)=2 so g(f(x))=1

    so......f of g = {(1,1),(2,1),(3,2),(4,1)}

    Is this correct?

    Yes, your numbers are correct. However, f of g is not g of f (in your last line you have written f of g not g of f).
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  5. #5
    kro
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    Talking Thanks alot!

    Ohhh yeah....I meant g of f.
    Thanks alot for you help......FYI, I'm about to post another question that's kinda similar to this one except I have to find: f of f^-1
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