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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!