Let's evaluate the given expressions step by step using the table provided.

Part (a): $(f \circ g)(1)$

The notation $(f \circ g)(1)$ means we first apply $g$ to $1$, then apply $f$ to the result.

1. From the table, find $g(1)$:

   • $g(1) = 11$ (look in the row labeled $g(x)$ under $x = 1$).

2. Next, find $f(g(1)) = f(11)$:

   • $f(11) = 1$ (look in the row labeled $f(x)$ under $x = 11$).

Thus, $(f \circ g)(1) = 1$.

Part (b): $(g \circ f)(0)$

The notation $(g \circ f)(0)$ means we first apply $f$ to $0$, then apply $g$ to the result.

1. From the table, find $f(0)$:

   • $f(0) = 9$ (look in the row labeled $f(x)$ under $x = 0$).

2. Next, find $g(f(0)) = g(9)$:

   • $g(9) = -10$ (look in the row labeled $g(x)$ under $x = 9$).

Thus, $(g \circ f)(0) = -10$.

Final Answers:

a. $(f \circ g)(1) = 1$
b. $(g \circ f)(0) = -10$

Do you need further clarification or a step-by-step explanation? Let me know!

Here are five related questions to expand your understanding:

1. How do you evaluate $(g \circ g)(1)$ using the table?
2. What is $(f \circ f)(-3)$?
3. Can you determine $(g \circ f)(4)$?
4. What is the general process for composition of functions?
5. Why does the order of composition matter when combining functions?

Tip: When working with composition of functions, always start from the innermost function and work outward!