To find the ordered pairs for the inverse of the function \( f(x) = x + 2 \), we need to follow these steps:
- Identify given ordered pairs from the function \( f(x) = x + 2 \).
- The points for the function can be expressed as \( (x, f(x)) = (x, x + 2) \).
- For the inverse, we swap the x and y coordinates of each ordered pair.
Let's calculate some points for the original function:
- \( f(-1) = -1 + 2 = 1 \) gives the point \( (-1, 1) \)
- \( f(0) = 0 + 2 = 2 \) gives the point \( (0, 2) \)
- \( f(1) = 1 + 2 = 3 \) gives the point \( (1, 3) \)
- \( f(2) = 2 + 2 = 4 \) gives the point \( (2, 4) \)
- \( f(3) = 3 + 2 = 5 \) gives the point \( (3, 5) \)
- \( f(4) = 4 + 2 = 6 \) gives the point \( (4, 6) \)
- \( f(5) = 5 + 2 = 7 \) gives the point \( (5, 7) \)
Now we can swap the coordinates to find the corresponding points for the inverse function:
- \( (-1, 1) \) becomes \( (1, -1) \)
- \( (0, 2) \) becomes \( (2, 0) \)
- \( (1, 3) \) becomes \( (3, 1) \)
- \( (2, 4) \) becomes \( (4, 2) \)
- \( (3, 5) \) becomes \( (5, 3) \)
From this set of points, the proper choice would include the pairs that correctly represent the coordinates of the original function swapped, which would not include any duplications or incorrect values.
To find which of the responses is correct:
- The response must include the points where the x and y have been swapped, resulting from the function \( (x + 2) \)
- So the correct ordered pairs for the inverse are \( {(1, -1), (2, 0), (3, 1), (4, 2), (5, 3)} \).
Reviewing the options:
- The correct answer can be matched against looking for pairs that have x-values related to \( f(x) \) switched correctly with the proper y-values.
The closest selection that shows inversed coordinates and is reasonable for the calculation should reflect switching on valid calculations in relations.
Therefore, the correct answer among given choices needs to be chosen. Please select the option which contains matching pairs to be analyzed into set values.
Considering our analysis, there is no exact response sent in, but you would write:
- The provided options should be glued to \( {(1, -1), (2, 0), (3, 1), (4, 2), (5, 3)} \) which through swaps won't be covered. Kindly select from pairs considering their match to verified swaps, if leading to close pairs reflecting correctly swapped values.