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Math Help - difficulty with one-to-ones

  1. #1
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    difficulty with one-to-ones

    okay, my professor did teach me this but he was hard to understand (due to having a foreign accent) when he tried to explain.

    so if someone could show me what to do with this problem, I would be so grateful.

    Problem:

    If g is one-to-one and g(12)=1, then g^(-1)=(12) and (g(12))^(-1) =___
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  2. #2
    Senior Member mollymcf2009's Avatar
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    Quote Originally Posted by lsnyder View Post
    okay, my professor did teach me this but he was hard to understand (due to having a foreign accent) when he tried to explain.

    so if someone could show me what to do with this problem, I would be so grateful.

    Problem:

    If g is one-to-one and g(12)=1, then g^(-1)=(12) and (g(12))^(-1) =___
    Problem:
    If g is one to one,

    g(12) = 1
    g^{-1} = 12
    (g(12))^{-1} = ?

    Hello!
    I assume that you have learned the properties of inverse functions? Each of these conditions given to you can be calculated if you know your inverse function rules. Here's a quickie review:
    1) For a function to have an inverse, it must be a one-to-one function.
    2) If g(x) is the inverse of f(x), then f(x) is the inverse of g(x).
    3) The domain of f(x) is equal to the range of  f^{-1}(x); the range of f(x) is equal to the domain of f^{-1}(x)**Think about what this mean when you have given (x, y) values. If you are given an (x,y) coordinate for your graph of f(x), don't you also have a coordinate on your graph of f^{-1}(x)? Think about it!!

    You can plot a few point from your given info right? See what you can come up with based on the above information! **Inverse functions will not go away, you will see them from now on in any college math class, gotta learn 'em**
    Ok? Good luck!
    Last edited by mollymcf2009; February 3rd 2009 at 05:41 PM. Reason: forgot to LaTex it oops...
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  3. #3
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    Quote Originally Posted by lsnyder View Post

    Problem:

    If g is one-to-one and g(12)=1, then g^(-1)=(12) and (g(12))^(-1) =___
    g^{-1}(12) =1

    because of this fact:

    If g is one-to-one and g(12)=1

    do you see why?
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