Question

Table 1
f (x)
-1
-12
1
-2
3
And
x
4
5
-2
6
-12

Table 2
g(x)
-1
-8
0
-5
1
And
x
-2
2
1
3
4

What is the Solution Set?

{?,?}

Answer 1

To find the solution set for the given tables, we need to identify the values of \( x \) where \( f(x) = g(x) \).

From Table 1, we have:

| \( x \) | \( f(x) \) |
|---------|------------|
| 4 | -1 |
| 5 | -12 |
| -2 | 1 |
| 6 | -2 |
| -12 | 3 |

From Table 2, we have:

| \( x \) | \( g(x) \) |
|---------|------------|
| -2 | -1 |
| 2 | -8 |
| 1 | 0 |
| 3 | -5 |
| 4 | 1 |

Now let's list the values of \( f(x) \) and \( g(x) \):

For \( f(x) \):
- \( f(4) = -1 \)
- \( f(5) = -12 \)
- \( f(-2) = 1 \)
- \( f(6) = -2 \)
- \( f(-12) = 3 \)

For \( g(x) \):
- \( g(-2) = -1 \)
- \( g(2) = -8 \)
- \( g(1) = 0 \)
- \( g(3) = -5 \)
- \( g(4) = 1 \)

Next, we will compare the values:

1. **For \( x = 4 \)**:
- \( f(4) = -1 \) and \( g(4) = 1 \) → not equal

2. **For \( x = 5 \)**:
- \( f(5) = -12 \) and doesn't exist in \( g(x) \) → not equal

3. **For \( x = -2 \)**:
- \( f(-2) = 1 \) and \( g(-2) = -1 \) → not equal

4. **For \( x = 6 \)**:
- \( f(6) = -2 \) and doesn't exist in \( g(x) \) → not equal

5. **For \( x = -12 \)**:
- \( f(-12) = 3 \) and doesn't exist in \( g(x) \) → not equal

6. **For \( x = 2 \)**:
- doesn't exist in \( f(x) \) → not equal

7. **For \( x = 1 \)**:
- doesn't exist in \( f(x) \) → not equal

8. **For \( x = 3 \)**:
- doesn't exist in \( f(x) \) → not equal

From our evaluation, the only \( x \) values that overlap the output of \( f \) and \( g \) result in no matches.

Thus, based on the provided values from both tables, there are no common \( x \) values where \( f(x) = g(x) \), leading us to conclude:

The solution set is \( \{ \} \) (an empty set).

If you are looking for explicitly asking to represent it in a specific format, such as {?,?}, we can simplify this to just \( \{\} \).