2. (12 points) The sequence of functions is defined by the formulas:

$$
f_{0}(x)=2 \sqrt{x}, f_{n+1}(x)=\frac{4}{2-f_{n}(x)}, n=0,1,2 \ldots, x \in[4 ; 9]
$$

Find $f_{2023}(4)$.
Answer: -2.

Solution. It is easy to calculate that $f_{3}(x)=f_{0}(x)$, therefore

$$
f_{2023}(x)=f_{1}(x)=\frac{2}{1-\sqrt{x}}
$$

Then $f_{2023}(4)=-2$.

Remark. One can immediately compute the values of the functions at the given point. The sequence will be $f_{0}(4)=4, f_{1}(4)=-2, f_{2}(4)=1, f_{3}(4)=4 \ldots$

Evaluation criteria. A fully justified solution - 12 points. Calculation errors - minus 1 point. The relation $f_{3}(x)=f_{0}(x)$ found - 7 points, the equality $f_{2023}(x)=f_{1}(x)$ found - another 4 points.