Why does this not work for finding the Maclaurin series of this expression?

Question

Okay, so I supposed to find the Maclaurin serie for the xpression $g(x)=e^{1-x}$. I thought I could use a well-know Maclaurin serie: $$\sum_{n=0}^{\infty} \frac{t^n}{n!}=e^t$$ and then just substitute for $t=1-x$. But my teacher said this do not work, but why? Can one only use substitution when the only thing you want to change is a factor in front of $x$?

Answer 1

Note that $$e^{1-x}= e(e^{-x})$$

$$e^{-x} = \sum_{n=0}^{\infty} \frac{(-x)^n}{n!}$$

You can take it from there.