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Math Help - One to One functions

  1. #1
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    One to One functions

    If f and g are one-to-one functions where f(-7)=6, F(2)=9 and g(-7)=9, then find-

    a)g of f^-1(6)

    b)f of g^-1(9)

    c)f^-1 of g(-7)

    I'm confused as to what goes where? I know how to compose functions, but this is confusing to me?
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  2. #2
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    Quote Originally Posted by Chinnie15 View Post
    If f and g are one-to-one functions where f(-7)=6, F(2)=9 and g(-7)=9, then find-

    a)g of f^-1(6)

    b)f of g^-1(9)

    c)f^-1 of g(-7)

    I'm confused as to what goes where? I know how to compose functions, but this is confusing to me?
    Remember that when you have inverse functions, the x and y values swap.

    So if f(-7) = 6 then f^{-1}(6) = -7.

    If F(2) = 9 then F^{-1}(9) = 2.

    If g(-7) = 9 then g^{-1}(9) = -7.


    So to answer your questions...

    a) g\left(f^{-1}(6)\right) = g(-7) = 9.


    b) f\left(g^{-1}(9)\right) = f(-7) = 6.


    c) f^{-1}\left(g(-7)\right) = f^{-1}(9).

    Since we do not have any information about f^{-1}(9) we can not go any further.
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  3. #3
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    Ok, I think I get it now. Thanks!
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