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Thread: 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 $\displaystyle x$ and $\displaystyle y$ values swap.

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

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

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


    So to answer your questions...

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


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


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

    Since we do not have any information about $\displaystyle f^{-1}(9)$ 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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