Use the table to answer the question.

Question

Table of x and g(x) Values
x −8
−7
6 10 15
g(x) 0 8 4 −5
−7
Which of the following options shows the domain of g−1(x)
?

(1 point)
Responses

{−7,−5,0,4,8}
left brace negative 7 comma negative 5 comma 0 comma 4 comma 8 right brace

{−8,−7,6,10,15}
left brace negative 8 comma negative 7 comma 6 comma 10 comma 15 right brace

{−8,−4,0,5,7}
left brace negative 8 comma negative 4 comma 0 comma 5 comma 7 right brace

{−15,−10,−6,7,8}
left brace negative 15 comma negative 10 comma negative 6 comma 7 comma 8 right brace
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Answer 1

To determine the domain of the inverse function \( g^{-1}(x) \), we need to identify the range of the original function \( g(x) \). The range consists of the output values (g(x) values) for the corresponding x values.

From the table provided:

• For \( x = -8 \), \( g(-8) = 0 \)
• For \( x = -7 \), \( g(-7) = 8 \)
• For \( x = 6 \), \( g(6) = 4 \)
• For \( x = 10 \), \( g(10) = -5 \)
• For \( x = 15 \), \( g(15) = -7 \)

The outputs (or g(x) values) from the table are:

• \( 0 \)
• \( 8 \)
• \( 4 \)
• \( -5 \)
• \( -7 \)

Thus, the range of \( g(x) \) is: \[ {-7, -5, 0, 4, 8} \]

This range becomes the domain of the inverse function \( g^{-1}(x) \).

Therefore, the correct option that represents the domain of \( g^{-1}(x) \) is: \[ { -7, -5, 0, 4, 8 } \]

So the answer is: \[ { -7, -5, 0, 4, 8 } \]