Question

The table shows values for functions f(x) and g(x).

x f(x)=2x−1 g(x)=12x
−2 −34 −1
−1 −12 −12
0 0 0
1 1 12
2 3 1
What is the solution to f(x)=g(x) ?

Select each correct answer.

Responses

x = −2
x = negative 2

x = −1
x = − 1

x = 0
x = 0

x = 1
x = 1

x = 2

Answer 1

To find the solution to \( f(x) = g(x) \), we need to compare the values of \( f(x) \) and \( g(x) \) for each given \( x \).

Here are the provided function values from the table:

\[
\begin{array}{|c|c|c|}
\hline
x & f(x) & g(x) \\
\hline
-2 & -34 & -1 \\
-1 & -12 & -12 \\
0 & 0 & 0 \\
1 & 1 & 12 \\
2 & 3 & 1 \\
\hline
\end{array}
\]

Now let's check for \( f(x) = g(x) \):

1. For \( x = -2 \):
- \( f(-2) = -34 \)
- \( g(-2) = -1 \)
- \( f(-2) \neq g(-2) \)

2. For \( x = -1 \):
- \( f(-1) = -12 \)
- \( g(-1) = -12 \)
- \( f(-1) = g(-1) \) (This is a solution)

3. For \( x = 0 \):
- \( f(0) = 0 \)
- \( g(0) = 0 \)
- \( f(0) = g(0) \) (This is another solution)

4. For \( x = 1 \):
- \( f(1) = 1 \)
- \( g(1) = 12 \)
- \( f(1) \neq g(1) \)

5. For \( x = 2 \):
- \( f(2) = 3 \)
- \( g(2) = 1 \)
- \( f(2) \neq g(2) \)

The solutions where \( f(x) = g(x) \) are:

- \( x = -1 \)
- \( x = 0 \)

Thus, the correct answers are:

- x = −1
- x = 0