Epimorphism from Polynomial Forms to Polynomial Functions

Theorem
Let $$D$$ be an integral domain.

Let $$D \left[{X}\right]$$ be the ring of polynomial forms in $$X$$ over $$D$$.

Let $$P \left({D}\right)$$ be the ring of polynomial functions over $$D$$.

The mapping $$\kappa: D \left[{X}\right] \to P \left({D}\right)$$ given by $$\kappa \left({\sum_{k=0}^n {a_k \circ X^k}}\right) = f$$

where $$f = \sum_{k=0}^n {a_k \circ x^k}, x \in D$$

is a ring epimorphism.