Question

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

x f(x)=2−x g(x)=−2x
−3 8 6
−2 4 4
−1 2 2
0 1 0
1 12 −2
2 14 −4
3 18 −6


What is the solution to f(x)=g(x) ?

Select each correct answer.



Responses

x=−3
x equals negative 3

x=−2
x equals negative 2

x=−1
x equals negative 1

x = 0
x = 0

x = 1
x = 1

x = 2
x = 2

x = 3

Answer 1

To find the solution to the equation \( f(x) = g(x) \), we can compare the values of the two functions \( f(x) \) and \( g(x) \) from the provided table. We need to identify the values of \( x \) where both functions have the same output.

From the table, we have:

\[
\begin{array}{|c|c|c|}
\hline
x & f(x) & g(x) \\
\hline
-3 & 8 & 6 \\
-2 & 4 & 4 \\
-1 & 2 & 2 \\
0 & 1 & 0 \\
1 & 12 & -2 \\
2 & 14 & -4 \\
3 & 18 & -6 \\
\hline
\end{array}
\]

Now let's check each \( x \) value to see where \( f(x) = g(x) \):

- For \( x = -3 \): \( f(-3) = 8 \), \( g(-3) = 6 \) (not equal)
- For \( x = -2 \): \( f(-2) = 4 \), \( g(-2) = 4 \) (equal)
- For \( x = -1 \): \( f(-1) = 2 \), \( g(-1) = 2 \) (equal)
- For \( x = 0 \): \( f(0) = 1 \), \( g(0) = 0 \) (not equal)
- For \( x = 1 \): \( f(1) = 12 \), \( g(1) = -2 \) (not equal)
- For \( x = 2 \): \( f(2) = 14 \), \( g(2) = -4 \) (not equal)
- For \( x = 3 \): \( f(3) = 18 \), \( g(3) = -6 \) (not equal)

The values of \( x \) for which \( f(x) = g(x) \) are:

- \( x = -2 \)
- \( x = -1 \)

Therefore, the correct answers are:

- \( x = -2 \)
- \( x = -1 \)