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Math Help - restriction

  1. #1
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    restriction

    Give a restriction on the function y=f(x)=ax2+bx+c so that its inverse f-1 exists, is either strictly increasing throughout its domain, or strictly decreasing, and so that no larger domain possesses these properties.
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  2. #2
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    Re: restriction

    Quote Originally Posted by franios View Post
    Give a restriction on the function y=f(x)=ax2+bx+c so that its inverse f-1 exists, is either strictly increasing throughout its domain, or strictly decreasing, and so that no larger domain possesses these properties.
    Inverse functions only exist when the original function is one-to-one. Since it's a quadratic, it will be one-to-one (and in this case, strictly increasing/decreasing) from the turning point on in either direction (but not both).
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