Question

What is the domain of h−1(x)
ℎ
−
1
(
𝑥
)
if h(x)={(−1,4),(0,5),(1,−6),(3,8)}
ℎ
(
𝑥
)
=
{
(
−
1
,
4
)
,
(
0
,
5
)
,
(
1
,
−
6
)
,
(
3
,
8
)
}
?(1 point)
Responses

{−1,0,1,3}
{
−
1
,
0
,
1
,
3
}
left brace negative 1 comma 0 comma 1 comma 3 right brace

{−6,4,5,8}
{
−
6
,
4
,
5
,
8
}
left brace negative 6 comma 4 comma 5 comma 8 right brace

{−8,−5,−4,6}
{
−
8
,
−
5
,
−
4
,
6
}
left brace negative 8 comma negative 5 comma negative 4 comma 6 right brace

{−3,−1,0,1}

Answer 1

To find the domain of the inverse function \( h^{-1}(x) \), we need to determine the range of the original function \( h(x) \).

Given \( h(x) = \{(-1, 4), (0, 5), (1, -6), (3, 8)\} \), we can see that the pairs are in the form \( (x, h(x)) \).

The values of \( h(x) \) are:
- \( h(-1) = 4 \)
- \( h(0) = 5 \)
- \( h(1) = -6 \)
- \( h(3) = 8 \)

The range of \( h(x) \) consists of the \( y \)-values (outputs) which are: \( 4, 5, -6, 8 \).

Thus, the domain of \( h^{-1}(x) \) is exactly the same as the range of \( h(x) \).

So the domain of \( h^{-1}(x) \) is \( \{ -6, 4, 5, 8 \} \).

The correct response is:
\[
\{ -6, 4, 5, 8 \}
\]