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Math Help - Please Check My Work:

  1. #1
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    Thumbs up Please Check My Work:

    Thanks!!

    -qbkr21
    Attached Thumbnails Attached Thumbnails Please Check My Work:-54.gif  
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by qbkr21 View Post
    Thanks!!

    -qbkr21
    Maybe I'm being a little dense. How did you know that f^{-1}(2) = 1?

    -Dan
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  3. #3
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by topsquark View Post
    Maybe I'm being a little dense. How did you know that f^{-1}(2) = 1?

    -Dan
    For problems like these, you are usually given functions where you can tell what the inverse of a particular number is. it is almost obvious to see that f^{-1}(2) = 1 just by looking at f(x) and mentally plugging in values and working backwards. however, if that does not suffice you, note that f^{-1}(2) is the solution to the following equation:

    f(x) = x^5 - x^3 + 2x = 2

    \Rightarrow x^5 - x^3 + 2x - 2 = 0

    \Rightarrow (x - 1) \left( x^4 + x^3 + 2 \right) = 0

    \Rightarrow x = 1 \mbox { or } x^4 + x^3 + 2 = 0

    the last equation has no real solutions, so we take x = 1

    thus, f^{-1}(2) = 1


    EDIT: Oh, and, yes, it looks good, qbkr21
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  4. #4
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Jhevon View Post
    it is almost obvious to see that f^{-1}(2) = 1 just by looking at f(x) and mentally plugging in values and working backwards.
    Doh! (We really need a Homer smiley.)

    -Dan
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  5. #5
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    Re:

    Thanks Guys!!

    -qbkr21
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