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Math Help - Inv.Functions

  1. #1
    ADY
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    Inv.Functions

    Ok bit of help please guys - i think i'm just twisting myself in unnecessary knots!

    The function: g(x) = \frac{1}{9}(x - 3)^2 - 4 (6 \leq x \leq 9)

    Is the Domain [6,9] ?

    How can i then find the image set of g^-1 and its rule?

    Thank you
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  2. #2
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    Quote Originally Posted by ADY View Post
    Ok bit of help please guys - i think i'm just twisting myself in unnecessary knots!

    The function: g(x) = \frac{1}{9}(x - 3)^2 - 4 (6 \leq x \leq 9)

    Is the Domain [6,9] ?

    How can i then find the image set of g^-1 and its rule?

    Thank you
    Yes the domain is [6,9].

    The range can be found by finding f(6) and f(9).

    f(6) = -3 and f(9) = 0 so the range is [-3,0]

    When taking the inverse the the domain becomes the range and the range becomes the domain. Therefore the domain of g^{-1}(x) is [-3,0] and the range is [6,9]

    Let y = g(x)

    9(y+4) = (x-3)^2

    \pm 3\sqrt{y+4} = x-3

    x  = 3\pm 3\sqrt{y+4}.

    g^{-1}(x) = 3\pm 3\sqrt{x+4}

    To determine the sign find g^{-1}(0) = 9 = 3+3\sqrt{4} = 9. So we want the positive root:

    g^{-1}(x) = 3+3\sqrt{x+4}

    Domain: [-3,0]
    Range : [6,9]
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  3. #3
    ADY
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    So is range the same as image set?
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  4. #4
    ADY
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    Just to check in my calculator...graphing

    f(x) = \frac{1}{9}(x - 3)^2 - 4 (6 \leq x \leq 9)

    this is a parabola, so the inverse function, how should this look as when i put in

    g^{-1}(x) = 3+3\sqrt{x+4}

    why doesnt it look like the reverse?
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  5. #5
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    if u have the graph of the function then just consider ur y axxis as xaxis and viceversa (i.e rotate ur copy) and now see the graph thats how it wud luk like
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  6. #6
    ADY
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    Thats what i thought - so is e^(i*pi) answer wrong?
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  7. #7
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    answer to wat ....e^(i*pi) is equal to -1
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  8. #8
    ADY
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    yes?
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  9. #9
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    Quote Originally Posted by ADY View Post
    Thats what i thought - so is e^(i*pi) answer wrong?
    No, his/her second answer is correct.
    g^{-1}(x)=3\sqrt{x+4}+3

    The range of g is [-3,0] so that is the domain of g^{-1}
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  10. #10
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    Quote Originally Posted by corleone2463 View Post
    answer to wat ....e^(i*pi) is equal to -1
    I think he meant the person using the forumname e^{i\pi}!
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