Inverses Represented Graphically Quick Check

Question

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

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
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Answer 1

To find the inverse of a function represented by a set of ordered pairs, we need to swap the elements in each pair.

Given: \[ F(x) = {(2,3),(1,-1),(−2,−2)} \]

The inverse \( F^{-1}(x) \) would be:

• From \( (2, 3) \) we get \( (3, 2) \)
• From \( (1, -1) \) we get \( (-1, 1) \)
• From \( (-2, -2) \) we get \( (-2, -2) \) (this one does not change)

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

Now, we can look at your options to find the one that matches:

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

The correct answer is: \( F^{-1}(x) = {(3, 2), (-1, 1), (-2, -2)} \).