# Math Help - functions and linear transformation

1. ## functions and linear transformation

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.

2. ## Re: functions and linear transformation

Originally Posted by widenerl194
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?