Question

Use the tables to answer the question.

x f(x)

−1
−12

1 −2

3 4
5 −2

6 −12

x g(x)

−1
−8

0 −5

1 −2

2 1
3 4
The tables represent the functions in the equation f(x)=g(x)
. What is the solution set?

(1 point)
The solution set is {
,
}.

Answer 1

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

From the first table for \( f(x) \):

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

From the second table for \( g(x) \):

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

Now we will look for \( x \) values such that \( f(x) = g(x) \).

1. For \( x = -1 \):
- \( f(-1) = -12 \)
- \( g(-1) = -8 \)
- Not equal.

2. For \( x = 1 \):
- \( f(1) = -2 \)
- \( g(1) = -2 \)
- Equal, so \( x = 1 \) is a solution.

3. For \( x = 3 \):
- \( f(3) = 4 \)
- \( g(3) = 4 \)
- Equal, so \( x = 3 \) is a solution.

4. For \( x = 5 \):
- \( f(5) = -2 \)
- Not in \( g(x) \).

5. For \( x = 6 \):
- Not in \( g(x) \).

The only values of \( x \) where \( f(x) = g(x) \) are 1 and 3.

Thus, the solution set is:
\[
\{ 1, 3 \}
\]