Let's solve the problems based on the tables provided in your image. The tables give us values for the functions $f(x)$, $g(x)$, and $h(x)$.

Table Summary:

• $f(x)$ table: \hline x & f(x) \\ \hline 0 & 1 \\ 1 & 5 \\ 2 & 9 \\ 3 & 13 \\ \hline \end{array}$$
• $g(x)$ table: \hline x & g(x) \\ \hline 5 & 5 \\ 7 & 10 \\ 9 & 15 \\ 11 & 20 \\ \hline \end{array}$$
• $h(x)$ table: \hline x & h(x) \\ \hline 5 & 0 \\ 10 & 2 \\ 15 & 5 \\ 20 & 9 \\ \hline \end{array}$$

Problem Solutions:

7. Find $f(1)$:

   • From the $f(x)$ table, when $x = 1$, $f(1) = 5$.

8. Find $g(5)$:

   • From the $g(x)$ table, when $x = 5$, $g(5) = 5$.

9. Find $g(f(1))$:

   • First, we find $f(1)$ from the $f(x)$ table. As calculated in problem 7, $f(1) = 5$.
   • Now find $g(5)$ from the $g(x)$ table. From problem 8, $g(5) = 5$.
   • Therefore, $g(f(1)) = 5$.

10. Find $g(9)$:

    • From the $g(x)$ table, when $x = 9$, $g(9) = 15$.

11. Find $h(15)$:

    • From the $h(x)$ table, when $x = 15$, $h(15) = 5$.

12. Find $h(g(9))$:

    • First, we find $g(9)$ from the $g(x)$ table. From problem 10, $g(9) = 15$.
    • Now find $h(15)$ from the $h(x)$ table. From problem 11, $h(15) = 5$.
    • Therefore, $h(g(9)) = 5$.

Would you like more details or clarification on any of these?

Here are 5 additional questions you can explore:

1. What is $f(3)$?
2. Can you find $h(10)$?
3. If $g(x)$ was extended, what could be the value of $g(13)$?
4. What would happen if we swapped the values for $h(x)$ and re-evaluated the problems?
5. How would you write $g(f(x))$ in terms of compositions for these values?

Tip: Function composition involves using the output of one function as the input for another—understanding this process will help in multi-step problems like these!