Which of the following options shows the inverse of F(x)={(2,3),(1,−1), (−2,−2)}

Question

?(1 point)
Responses

F−1(x)={(−3,−2),(1,−1), (2,2)}
upper F inverse left parenthesis x right parenthesis equals left brace left parenthesis negative 3 comma negative 2 right parenthesis comma left parenthesis 1 comma negative 1 right parenthesis comma left parenthesis 2 comma 2 right parenthesis right brace

F−1(x)={(2,−3),(1,1), (−2,2)}
upper F inverse left parenthesis x right parenthesis equals left brace left parenthesis 2 comma negative 3 right parenthesis comma left parenthesis 1 comma 1 right parenthesis comma left parenthesis negative 2 comma 2 right parenthesis right brace

F−1(x)={(−2,3),(−1,−1), (2,−2)}
upper F inverse left parenthesis x right parenthesis equals left brace left parenthesis negative 2 comma 3 right parenthesis comma left parenthesis negative 1 comma negative 1 right parenthesis comma left parenthesis 2 comma negative 2 right parenthesis right brace

F−1(x)={(3,2),(−1,1), (−2,−2)}
upper F inverse left parenthesis x right parenthesis equals left brace left parenthesis 3 comma 2 right parenthesis comma left parenthesis negative 1 comma 1 right parenthesis comma left parenthesis negative 2 comma negative 2 right parenthesis right brace

Answer 1

To find the inverse of the function \( F(x) = {(2,3), (1,-1), (-2,-2)} \), we need to swap the ordered pairs. The inverse function \( F^{-1}(x) \) will consist of the pairs where the first element becomes the second element and the second becomes the first.

Let's perform the transformation on each pair:

1. \( (2, 3) \) becomes \( (3, 2) \)
2. \( (1, -1) \) becomes \( (-1, 1) \)
3. \( (-2, -2) \) becomes \( (-2, -2) \)

Thus, the inverse function is:

\[ F^{-1}(x) = {(3, 2), (-1, 1), (-2, -2)} \]

Now let's compare this with the provided options:

1. \( F^{-1}(x) = {(-3, -2), (1, -1), (2, 2)} \)
2. \( F^{-1}(x) = {(2, -3), (1, 1), (-2, 2)} \)
3. \( F^{-1}(x) = {(-2, 3), (-1, -1), (2, -2)} \)
4. \( F^{-1}(x) = {(3, 2), (-1, 1), (-2, -2)} \)

The fourth option matches our calculated inverse.

Therefore, the correct answer is:

\( F^{-1}(x) = {(3, 2), (-1, 1), (-2, -2)} \)