1. Let the function $f(x)$ have a domain of $[-4,+\infty)$, and satisfy that for any real number $t$, $f\left(t^{2}+4 t\right)=|t+2|$, then the analytical expression of $f(x)$ is $f(x)=$ $\qquad$ .
$$
f\left(t^{2}+4 t\right)=\sqrt{t^{2}+4 t+4} \Rightarrow f(x)=\sqrt{x+4}
$$

The solution is as follows:
$$
f\left(t^{2}+4 t\right)=\sqrt{t^{2}+4 t+4} \Rightarrow f(x)=\sqrt{x+4}
$$