Here is my problem:

Let $\Pi\_2$ be the function space of all polynomials of max. grade 2,that are defined on the interval $[-1,1]$.

Let $G : \Pi\_2 \to \mathbb{R}$ be given as $f \stackrel{G}{\mapsto} f(1) $. 

What is the basis of the $\ker(G)$ ?

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My thoughts process is to find the set of the kernel and then find the basis to it.

The kernel is the set of functions which evaluate to zero. So:

$\ker(G):= \{ \ f \ | \ f(1) = 0\} $ I dont know how to write this set more formally.

My next step would be to find the basis to this set.

<https://en.wikipedia.org/wiki/Kernel_(linear_algebra)#Examples>