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Can you solve it?

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    Yes, I can. But I'm not just going to give you the answer - show your working.

    Edit: When I posted this I wasn't anticipating that others would 'join in' - I'm actually trying to help, so if you post your working I'll let you know where you're going wrong or give you some pokes in the right direction.
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    Is this something like a questionnaire? I think I can solve it.
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    No
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    I can, however nuodai summed it up quite well
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    Yeah I can.
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    Yep, but it would ruin the fun of Maths for you if I did it, wouldn't it?
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    (Original post by nuodai)
    Yes, I can. But I'm not just going to give you the answer - show your working.

    Edit: When I posted this I wasn't anticipating that others would 'join in' - I'm actually trying to help, so if you post your working I'll let you know where you're going wrong or give you some pokes in the right direction.
    (a) f(x) = (1-x^2)^1/2 & f(x) = -((1-x^2)^1/2)
    (b) no function exists with such a property
    (c) Click image for larger version. 

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    (Original post by math1234)
    (a) f(x) = (1-x^2)^1/2 & f(x) = -((1-x^2)^1/2)
    (b) no function exists with such a property
    (c) Click image for larger version. 

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    Your answers for (a) and (b) are correct from what I can tell. But I don't understand your solution to (c); what is g(x), for instance?
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    (Original post by nuodai)
    Your answers for (a) and (b) are correct from what I can tell. But I don't understand your solution to (c); what is g(x), for instance?
    Click image for larger version. 

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    g_1, g_2, g_3 = g_i
    g(f(x))=x
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    why not you guys are now making fun of my post?(except nuodai) the reason is because you don't understand this question.
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    (Original post by math1234)
    Click image for larger version. 

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    g_1, g_2, g_3 = g_i
    g(f(x))=x
    Right, so it's a piecewise inverse to the cubic. That's right.

    Your answers all seem fine. Where were you having problems?
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    (Original post by nuodai)
    Right, so it's a piecewise inverse to the cubic. That's right.

    Your answers all seem fine. Where were you having problems?
    how can we find y=f_i (x) =g_i^-1 (x) explicitly? & on what intervals g are one-one contained: (-infinity, -1) or (-1, 1) or (1, infinity)?

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