Question

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

x f(x)=2x−4 g(x)=32x−3
−1 −7/2 −9/2
0 −3 −3
1 −2 −3/2
2 0 0
3 4 3/2
4 12 3
5 28 9/2


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

Select each correct answer.



Responses

x=−1
x equals negative 1

x = 0
x = 0

x = 1
x = 1

x = 2
x = 2

x = 3
x = 3

x = 4
x = 4

x = 5
x = 5

Answer 1

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

Let's examine the table:

\[
\begin{array}{|c|c|c|}
\hline
x & f(x) & g(x) \\
\hline
-1 & -\frac{7}{2} & -\frac{9}{2} \\
0 & -3 & -3 \\
1 & -2 & -\frac{3}{2} \\
2 & 0 & 0 \\
3 & 4 & \frac{3}{2} \\
4 & 12 & 3 \\
5 & 28 & \frac{9}{2} \\
\hline
\end{array}
\]

Now we will look for the values of \( x \) where \( f(x) \) is equal to \( g(x) \):

1. For \( x = -1 \): \( f(-1) = -\frac{7}{2} \) and \( g(-1) = -\frac{9}{2} \) (not equal)
2. For \( x = 0 \): \( f(0) = -3 \) and \( g(0) = -3 \) (equal)
3. For \( x = 1 \): \( f(1) = -2 \) and \( g(1) = -\frac{3}{2} \) (not equal)
4. For \( x = 2 \): \( f(2) = 0 \) and \( g(2) = 0 \) (equal)
5. For \( x = 3 \): \( f(3) = 4 \) and \( g(3) = \frac{3}{2} \) (not equal)
6. For \( x = 4 \): \( f(4) = 12 \) and \( g(4) = 3 \) (not equal)
7. For \( x = 5 \): \( f(5) = 28 \) and \( g(5) = \frac{9}{2} \) (not equal)

The solutions to \( f(x) = g(x) \) are \( x = 0 \) and \( x = 2 \).

Thus, the correct answers are:

- x = 0
- x = 2