3. Find the linear function $f(x)$ that satisfies the inequality $f[f(x)] \geqslant x-3, x \in \mathbf{R}$.
3. Using the method of undetermined functions. Let $f(x)=a x+b, a, b \in \mathbf{R}$, then
$$
f[f(x)]=a f(x)+b=a(a x+b)+b=a^{2} x+(a+1) b \geqslant x-3
$$

holds for all $x \in \mathbf{R}$. It must be that $a^{2}=1,(a+1) b \geqslant-3$, i.e., $a=-1, b \in \mathbf{R}$ or $a=1, b \geqslant-\frac{3}{2}$. Therefore, the solution to the given functional inequality is $f(x)=-x+b, b \in \mathbf{R}$ or $f(x)=x+b, b \geqslant-\frac{3}{2}$.