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Math Help - Inverse function of a closed set???

  1. #1
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    Inverse function of a closed set???

    This is a textbook problem...
    f:R->R
    f(x) = x^2
    (i)Find f^-1(25).
    (ii)Find f^-1([4, 25])
    The first one is easy but how do I do the 2nd one? I've never encountered something like this.
    I suppose
    Let f^-1([4,25])=x
    or, f(x)=[4,25]
    or, x^2=[4,25]
    ...and then?
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  2. #2
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    (ii)Find f^-1([4, 25])<br />

    This is just asking you to find all x in the domain taht get mapped into the interval [4,25]

    So x^2\in[4,25]

    So 2\leq x \leq 5 and also -5\leq x\leq -2 (all you do is take the positive and negative square root of the closed set interval)
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  3. #3
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    I was thinking something like that. Thanks. Seinfeld rules BTW(assuming that's where you got your name)
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