KöMaL 2022 C1742

Consider the following functions (defined on the largest possible subset of the set of real numbers): $f_0(x)=\frac{1}{1-x}, \text{and} f_n(x)=f_0\big(f_{n-1}(x)\big),$ for all positive integers $n$. Calculate the value of $f_{2022}(2022)$.