<s>[INST] Given $f(x+1)=x^2-3x+2$, how can I find $f(x)$? Given $f(x+1)=x^2-3x+2$, how can I find $f(x)$?
 [/INST] Let $y=x+1$. We then have $x=y-1$. Hence,
\begin{align}
f(y) & = f(x+1) = x^2 -3x+2 = (y-1)^2 - 3(y-1)+2\\
& = y^2-2y+1-3y+3+2 = y^2-5y+6
\end{align}
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