Question

Use the table to answer the question.

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

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

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

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

{−7,−5,0,4,8}

Answer 1

To determine the domain of the inverse function \( g^{-1}(x) \), we need to know the range of the original function \( g(x) \). The range is made up of the outputs of \( g(x) \).

From the given values:

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

The outputs (or the values of \( g(x) \)) are:
- \( 0 \)
- \( 8 \)
- \( 4 \)
- \( -5 \)
- \( -7 \)

Thus, the range of \( g(x) \), which corresponds to the domain of \( g^{-1}(x) \), is:
\[ \{-7, -5, 0, 4, 8\} \]

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