Inverses Represented Numerically Quick Check

Question

1 of 51 of 5 Items
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,−7,6,10,15}
left brace negative 8 comma negative 7 comma 6 comma 10 comma 15 right brace

{−7,−5,0,4,8}
left brace negative 7 comma negative 5 comma 0 comma 4 comma 8 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 find the domain of the inverse function \( g^{-1}(x) \), we need to look at the range of the original function \( g(x) \).

From the given table, we have:

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

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

Thus, the domain of \( g^{-1}(x) \) will be the same as the range of \( g(x) \).

Now we compare the options:

1. { −8,−7,6,10,15 } - This is the domain of \( g(x) \).
2. { −7,−5,0,4,8 } - This is the range of \( g(x) \) and therefore the domain of \( g^{-1}(x) \).
3. { −8,−4,0,5,7 } - This does not match the outputs.
4. { −15,−10,−6,7,8 } - This does not match the outputs.

The correct answer is:

{−7,−5,0,4,8}