Taylor polynomial/R/Dilation/Exercise

Let ${}f\colon \mathbb {R} \rightarrow \mathbb {R}$ be an ${}n$-fold differentiable function in the point ${}a$. Show that the ${}n$-th Taylor polynomial for ${}f$ in the point ${}a$, written in the shifted variable ${}x-a$, equals the ${}n$-th Taylor polynomial of the function ${}g(x)=f(x+a)$ in the zero point.

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