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Determine which two relations are inverses of each other based on their descriptions.(1 point)

Responses

The amount of water needed in terms of the temperature outside, and the number of breaks needed in terms of the number of hours spent outside.
The amount of water needed in terms of the temperature outside, and the number of breaks needed in terms of the number of hours spent outside.

The amount of water needed in terms of the temperature outside, and the temperature outside in terms of the number of breaks needed.
The amount of water needed in terms of the temperature outside, and the temperature outside in terms of the number of breaks needed.

The amount of water needed in terms of the temperature outside, and the amount of water needed in terms of the number of hours spent outside.
The amount of water needed in terms of the temperature outside, and the amount of water needed in terms of the number of hours spent outside.

The amount of water needed in terms of the temperature outside, and the temperature outside in terms of the amount of water needed.
The amount of water needed in terms of the temperature outside, and the temperature outside in terms of the amount of water needed.

1 answer

To determine which two relations are inverses of each other, we need to identify pairs of relations where one relation can be expressed in terms of another, and vice versa.

Looking at the provided pairs:

  1. The amount of water needed in terms of the temperature outside, and the number of breaks needed in terms of the number of hours spent outside.
  2. The amount of water needed in terms of the temperature outside, and the temperature outside in terms of the number of breaks needed.
  3. The amount of water needed in terms of the temperature outside, and the amount of water needed in terms of the number of hours spent outside.
  4. The amount of water needed in terms of the temperature outside, and the temperature outside in terms of the amount of water needed.

The best candidates for inverses are the fourth option: "The amount of water needed in terms of the temperature outside, and the temperature outside in terms of the amount of water needed."

This is because if you know the amount of water needed, you can determine the temperature outside, and vice versa. Therefore, these two relations are truly inverse functions of each other.