4. Let $f(x)=x^{2}+b x+c$, if the equation $f(x)=x$ has no real roots, then the equation $f(f(x))=x \quad(\quad)$
A. has 4 real roots
B. has 2 real roots
C. has 1 real root
D. has no real roots
4. D $f(x)=x$ has no real roots, which means the line $y=x$ does not intersect the parabola $y=f(x)$. Since the coefficient of the quadratic term in $f(x)$ is positive, we know the parabola opens upwards. Thus, the graph of $y=f(x)$ lies above the line $y=x$. That is, $f(x)>x$. Therefore, $f(f(x))>f(x)>x$.