4. The roots of the equation $x^{2}-x+1=0$ are $\alpha, \beta$. There is a quadratic function $f(x)$ that satisfies $f(\alpha)=\beta, f(\beta)=\alpha, f(1)=$ 1, then the expression of $f(x)$ is $\qquad$ .
4. $f(x)=x^{2}-2 x+2$

We can set $f(x)=a\left(x^{2}-x+1\right)+b x+c$, then $b \alpha+c=\beta, b \beta+c=\alpha$, $a+b+c=1, \alpha+\beta=1$, solving these we get $a=1, b=-1, c=1$.