https://file.aiquickdraw.com/mathbot/file/1725636889117jv0hdkq1.jpg

The image shows three functions \( f(x) \), \( g(x) \), and \( h(x) \) defined by their values in tables. Below that, there are two questions to solve:

1. \( f(h(1)) \)
2. \( g(f(0)) \)

I'll read the data from the tables to solve these.

From the table, the values for the functions are:
- \( f(x) \):
  - \( f(0) = 5 \)
  - \( f(1) = 9 \)
  - \( f(2) = 7 \)

- \( g(x) \):
  - \( g(0) = 7 \)
  - \( g(1) = 3 \)
  - \( g(2) = 4 \)

- \( h(x) \):
  - \( h(0) = 2 \)
  - \( h(1) = 0 \)
  - \( h(2) = 1 \)

### 1. Find \( f(h(1)) \):
- \( h(1) = 0 \), so we need to find \( f(0) \).
- From the table, \( f(0) = 5 \).
- Therefore, \( f(h(1)) = 5 \).

### 2. Find \( g(f(0)) \):
- From the table, \( f(0) = 5 \), but \( g(x) \) is only defined for values 0, 1, and 2, and does not include 5.
- Therefore, \( g(f(0)) \) is **undefined**.

Let me know if you'd like more details or further explanations.

### 5 Relative Questions:
1. How do we interpret the composition of functions from a table of values?
2. What happens if a function's input is outside the provided table?
3. How can we graph functions using tabulated data?
4. Can the process of function composition be generalized beyond specific values?
5. What other ways can functions be represented besides tables?

**Tip**: Always check if the function values fall within the defined domain before solving compositions of functions.

Evaluate the following functions given their values in a table: 1. f(h(1)), 2. g(f(0)).

Learn how to evaluate function compositions using tabulated data. This problem involves reading values from a table and calculating compositions such as f(h(1)) and g(f(0)). Suitable for students in Grades 6-8.

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