2. The range of the function $f(x)=x+\frac{4}{x}-\sqrt{-x^{2}+4 x-3}$ is $\qquad$ .
2. $[3,5]$.

From the problem, we know that the domain of $f(x)$ is $[1,3]$.
Notice that,
$$
g(x)=x+\frac{4}{x}, h(x)=-\sqrt{-x^{2}+4 x-3}
$$

are both monotonically decreasing on the interval $[1,2]$ and monotonically increasing on the interval $[2,3]$.

Therefore, $f(x)$ is monotonically decreasing on the interval $[1,2]$ and monotonically increasing on the interval $[2,3]$.

Given $f(1)=5, f(2)=3, f(3)=\frac{13}{3}$, we know that the range of $f(x)$ is $[3,5]$.