\(\left\{{}\begin{matrix}f\left(x\right)=ax+b\\g\left(x\right)=x^2-x+1\end{matrix}\right.\)
Từ giả thiết đề bài:
\(\left\{{}\begin{matrix}f\left(1\right)=g\left(2\right)\\f\left(-2\right)=g\left(1\right)\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}a+b=4-2+1=3\\-2a+b=1-1+1=1\end{matrix}\right.\)
\(\Rightarrow a+b+2a-b=2\)
\(\Rightarrow3a=2\Leftrightarrow a=\dfrac{2}{3}\)
\(b=3-\dfrac{2}{3}=\dfrac{7}{3}\)