The image contains a list of mathematical problems related to functions and their compositions. The functions $f(x)$ and $g(x)$ are defined as:

• $f(x) = \frac{x + 1}{x - 1}$
• $g(x) = \sqrt{x} - 2$

The questions ask to determine the values of the following operations, including inverse functions and compositions:

1. $f^{-1}(2)$
2. $g^{-1}(2)$
3. $g^{-1}(1)$
4. $f^{-1}(1)$
5. $(f \circ g)(2)$
6. $(g \circ f)(2)$
7. $(f \circ g)^{-1}(2)$
8. $(g \circ f)^{-1}(2)$
9. Given $h(x) = (x-1)^3$ and $h(x) = f \circ g$, determine $f$ and $g$.
10. Given $h(x) = \frac{x}{x^2 + 1}$ and $h(x) = f \circ g$, determine $f$ and $g$.
11. Given $h(x) = (x-3)^3$ and $h(x) = f \circ g$, determine $f$ and $g$.

Would you like me to begin solving these step by step?