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Math Help - functions again

  1. #1
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    Unhappy functions again

    on the same set of axes graph the curves 1+ (1/x) and 1/(x-1)
    describe a transformation that maps the first curve onto the second
    is there an algebraic way of doing this? well i'm sure there is, but can someone explain? how do you do that?
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  2. #2
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    Quote Originally Posted by the kopite View Post
    on the same set of axes graph the curves 1+ (1/x) and 1/(x-1)
    describe a transformation that maps the first curve onto the second
    is there an algebraic way of doing this? well i'm sure there is, but can someone explain? how do you do that?
    If f(x) = 1 + \frac{1}{x} then \frac{1}{x-1} = f(x - 1) - 1. So two translations have been applied ....
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  3. #3
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    was that supposed to be helpful?
    sorry but i really dont perceive any explanation to my problem.it seems to me that the answer is a reflection in y=x, but i'd like to understand why, algebraically. is that possible? matrices (???????)?
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  4. #4
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    Quote Originally Posted by the kopite View Post
    was that supposed to be helpful?
    [snip]
    Of course not. Why on Earth would I post something helpful? When I do it's only by accident.

    Quote Originally Posted by the kopite View Post
    [snip]
    sorry but i really dont perceive any explanation to my problem.
    [snip]
    My mistake. I assumed that you would be familiar with the functional representation of various transformations.

    Quote Originally Posted by the kopite View Post
    [snip]
    it seems to me that the answer is a reflection in y=x,
    [snip]
    Correct. But that answer is not unique. Another possible answer is the one I gave earlier. Horizontal translation of +1 units, vertical translation of +1 units.

    Quote Originally Posted by the kopite View Post
    [snip] but i'd like to understand why, algebraically. is that possible? matrices (???????)?
    Reflection in the line y = x is equivalent to finding the inverse ....
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  5. #5
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    Talking

    Quote Originally Posted by the kopite View Post
    it seems to me that the answer is a reflection in y=x, but i'd like to understand why, algebraically. is that possible?
    Yes: use function transormations and translations, as explained in the earlier solution.

    Since you are not familiar with function notation, etc, you must be expected to use some other method. But I'm afraid we can't know what method you're supposed to use until you tell us. Sorry!

    Note: Since matrices are generally covered well after basic algebra (such as function notation), you probably are not expected to use this methodology.

    When you reply with the method(s) you're supposed to use, please include a clear listing of what you have tried so far, so we can "see" where you are having trouble and then try to provide assistance that you might find useful.

    Thank you!
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  6. #6
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    now thats what i call helpful...! thank you both
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