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simpledude
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Homework Statement
Let V = P2(R) be the vector space of all polynomials P : R −> R that have order less
than 2. We consider the mapping F : V −> V defined for all P belonging to V , by
F(P(x)) = P'(x)+P(x) where
P'(x) denotes the first derivative of the polynomial P.
Question is: Show that F is an isomorphism from V into V
The Attempt at a Solution
So first I showed that F is a linear operator. Now I have to show Ker F={0}
However, when I start to solve the equation, I get lost at solving
P'(x) + P(x) = 0
I know this is a basic first order linear equation, can anyone point me in the right direction?
Thanks!