Use the table to answer the question.

Question

x −3
−1
0 1 3
f(x)
−10
−7
0 2 8
Which of the following is the inverse of the function given in the table?

(1 point)
Responses

x −10
−7
0 2 8
g(x)
−3
−1
0 1 3
x negative 10 negative 7 0 2 8 g left parenthesis x right parenthesis negative 3 negative 1 0 1 3

x −3
−1
0 1 3
g(x)
10 7 0 −2
−8
x negative 3 negative 1 0 1 3 g left parenthesis x right parenthesis 10 7 0 negative 2 negative 8

x 3 1 0 −1
−3
g(x)
10 7 0 −2
−8
x 3 1 0 negative 1 negative 3 g left parenthesis x right parenthesis 10 7 0 negative 2 negative 8

x 10 7 0 −2
−8
g(x)
−3
−1
0 1 3

Answer 1

To find the inverse of the function given in the table, we will swap the \(x\) and \(f(x)\) values.

The original function \(f(x)\) from the table is:

• \(f(-3) = -10\)
• \(f(-1) = -7\)
• \(f(0) = 0\)
• \(f(1) = 2\)
• \(f(3) = 8\)

To find the inverse \(g(x)\), we swap the values:

1. From \(f(-3) = -10\), we have \(g(-10) = -3\)
2. From \(f(-1) = -7\), we have \(g(-7) = -1\)
3. From \(f(0) = 0\), we have \(g(0) = 0\)
4. From \(f(1) = 2\), we have \(g(2) = 1\)
5. From \(f(3) = 8\), we have \(g(8) = 3\)

Putting those together, the inverse function \(g(x)\) can be summarized as:

\[ g(x) = \begin{cases} -3 & \text{if } x = -10 \ -1 & \text{if } x = -7 \ 0 & \text{if } x = 0 \ 1 & \text{if } x = 2 \ 3 & \text{if } x = 8 \ \end{cases} \]

Now we check the options given in your question.

The correct answer is:

Option 1: x −10 −7 0 2 8 g(x) −3 −1 0 1 3

So the inverse of the function given in the table is \(g(x) = -3, -1, 0, 1, 3\) for \(x = -10, -7, 0, 2, 8\) respectively.