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Use the table to answer the 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 10 7 0 negative 2 negative 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 −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 3 1 0 negative 1 negative 3 g left parenthesis x right parenthesis 10 7 0 negative 2 negative 8
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1 answer

To find the inverse of the function represented in the table, we swap the values of \(x\) and \(f(x)\). From the table:

| x | f(x) | |-----|------| | -3 | -10 | | -1 | -7 | | 0 | 0 | | 1 | 2 | | 3 | 8 |

To find the inverse \(g(x)\), we switch \(x\) and \(f(x)\):

| g(x) | x | |------|-----| | -10 | -3 | | -7 | -1 | | 0 | 0 | | 2 | 1 | | 8 | 3 |

Now, we write this as \(g(x)\):

| x | g(x) | |-----|------| | -10 | -3 | | -7 | -1 | | 0 | 0 | | 2 | 1 | | 8 | 3 |

We are looking for a response that matches this format. The provided choices are:

  1. \(x\) 10 7 0 -2 -8, \(g(x)\) -3 -1 0 1 3
  2. \(x\) -3 -1 0 1 3, \(g(x)\) 10 7 0 -2 -8
  3. \(x\) -10 -7 0 2 8, \(g(x)\) -3 -1 0 1 3
  4. \(x\) 3 1 0 -1 -3, \(g(x)\) 10 7 0 -2 -8

From our inverse definition, we can see that:

  • The first option does not match.
  • The second option does not match.
  • The third option correctly shows \(x\) values as -10, -7, 0, 2, 8 and corresponding \(g(x)\) values as -3, -1, 0, 1, 3.
  • The fourth option does not match.

Therefore, the correct answer is:

x -10 -7 0 2 8, g(x) -3 -1 0 1 3 which corresponds to option 3.