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Math Help - inverse function?

  1. #1
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    inverse function?

    The function f : [a, infinity) -> R with rule f (x) = 2x^3 − 3x^2 + 6 will have an inverse function provided?

    the answer was a >= 1,
    but why not also a <= 0?
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  2. #2
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    Quote Originally Posted by scorpion007 View Post
    The function f : [a, infinity) -> R with rule f (x) = 2x^3 − 3x^2 + 6 will have an inverse function provided?

    the answer was a >= 1,
    but why not also a <= 0?
    Hello, scorpion,

    as you know a function f has an inverse function if f is monotonously increasing or monotonously decreasing.
    So your function has 3 intervalls where f is monotonous:
    (-\infty;0],\ (0;1], (1,+\infty)

    So you are looking for a lower bound of the intervall which contains +infinity.

    With your suggestion you would look for the upper bound.

    EB

    I have to send you this post without checking my text because the preview doesn't work. So watch out: There are possibly some mistakes.
    Attached Thumbnails Attached Thumbnails inverse function?-umk_fkt1.gif  
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  3. #3
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    ahhh, thank you, i overlooked that fact! i see now
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  4. #4
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    Quote Originally Posted by earboth View Post
    as you know a function f has an inverse function if f is monotonously increasing or monotonously decreasing.
    Earboth, please understand I'm not picking on you, but that sentence just had me rolling on the floor.

    Monotonous: (definition) tediously uniform or unvarying.

    The word in English you were looking for is "monotonically."

    It very much reminds me of a lady at a school I once worked at. She was trying to make a poster thanking everyone who had contributed money to the school's fundraising campaign. She wrote "Thank you for patronizing us."

    For those who don't know, there are two definitions for the word "patronize"
    1) to act as patron of : provide aid or support for
    2) to adopt an air of condescension toward : treat haughtily or coolly

    Two VERY different meanings!

    -Dan
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  5. #5
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    I understand what earboth said, but formally there is no answer to your question!!

    A function,
    f:[a,\infty)\to \mathbb{R} would have an inverse if and only if f(x)=2x^3-3x^2+6, x\geq a is a bijective map. That means is is a surjective map. But for a\geq 1 the map is not sujective. Because if you chose y=0 there is no x\geq 1 such as, f(x)=0. What you should have said is,
    f:[a,\infty)\to [5,\infty)
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  6. #6
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    Quote Originally Posted by earboth View Post
    a function f has an inverse function if f is monotonously increasing or monotonously decreasing.
    Hello !

    I want only to emphasize that this is a sufficient condition, not a necessarily one !
    That's plenty of examples...
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  7. #7
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    Quote Originally Posted by misto View Post
    Hello !

    I want only to emphasize that this is a sufficient condition, not a necessarily one !
    That's plenty of examples...
    Give an example, I do not think I understand what you are saying.
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