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Math Help - functions and linear transformation

  1. #1
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    functions and linear transformation

    I'm not sure where to start with this:

    Define h: P2 --> P3 by h(p(x)) = xp'(x) + the integral from 0 to x of p(t) dt.

    a. Verify that the codomain of h is in fact P3 and prove that h is a linear transformation.
    b. Find h(p(x)) where p(x) = x2 + x + 1.
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  2. #2
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    Re: functions and linear transformation

    Quote Originally Posted by widenerl194 View Post
    Define h: P2 --> P3 by h(p(x)) = xp'(x) + the integral from 0 to x of p(t) dt.
    a. Verify that the codomain of h is in fact P3 and prove that h isis a linear transformation.
    b. Find h(p(x)) where p(x) = x2 + x + 1.
    If you are really serious then answer this question:
    h(ax^2+bx+c)=~?

    If you can do that then what is the generalization?
    Last edited by Plato; May 7th 2013 at 05:45 PM.
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