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    I thought I got it...but I haven't.



    I've completed part a. The answer being:



    I can find the RANGE of f^{-1} (x) since I know that is domain of f(x).

    However, to find the DOMAIN of f^{-1} (x) I need to know what the RANGE of of f(x) is and I don't know how to work that out.

    How do I find the DOMAIN of f^{-1} (x)?


    Do I have to sketch it? The graph is hard to sketch...Thank you for your help. Can I use this method where x - 2 =/= 0 and solve?
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    The graph of f(x) isn't hard to sketch: all you need to do is carry out long division on (2x + 3)/(x-1), then you'll get f(x) = m + n/(x-1) where m and n are just constants you can find, which is a C1 sketch.

    This is the best approach to find the domain of the inverse. It won't necessarily correspond with x =/= 2 because f(x) isn't defined for all values of x.
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    By division, I have: 2 + 5 / x - 1

    So the curve moves one unit to the right, meaning x > 2?
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    A technique that I use to tackle this question (although doesn't always work) is to draw a table of the x values and the y values.
    start at x=1 (because that's the domain) then y=infinity
    x=2 y=7
    x=3 y=4.5
    and so on then try it with a very large number like 1000000, then a bigger number. You should notice that it is tending to 2 but can never be 2, so that's the smallest number. so if the smallest number is tending to 2 and it goes towards infinity, hopefully you can work out the range.
    hope this helps, i also hate these questions.
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    (Original post by gottastudy)
    By division, I have: 2 + 5 / x - 1

    So the curve moves one unit to the right, meaning x > 2?
    :yes:
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    (Original post by Superman_Jr)
    :yes:
    Ok thank you!

    It's only chapter 2, so it can't be THAT hard surely, maybe I'm over complicating something and I'm just missing the point?
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    (Original post by gottastudy)
    Ok thank you!

    It's only chapter 2, so it can't be THAT hard surely, maybe I'm over complicating something and I'm just missing the point?
    Nah, it's not that hard....ITS SUICIDE!!!!!111 :eek3:
    I don't think you are, it is quite tricky if you're not thinking it through, but oh well...what can you do? :p:
 
 
 
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