Problem

\(T(h)\) gives temperature in degrees Celsius at height \(h\) meters on an interval where \(T\) is one-to-one. Describe the forward and inverse mappings with units, and explain the uniqueness condition.

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Forward: T maps height, in meters, to temperature, in degrees Celsius. Inverse: T⁻¹ maps height, in meters, to temperature, in degrees Celsius. Uniqueness follows on the stated interval.

Forward: T maps height, in square meters, to temperature, in meters. Inverse: T⁻¹ maps temperature θ, in meters, to the unique height, in square meters, where the temperature is θ. Uniqueness follows on the stated interval.

Forward: T maps height, in meters, to temperature, in degrees Celsius. Inverse: T⁻¹ maps temperature θ, in degrees Celsius, to the unique height, in meters, where the temperature is θ. Uniqueness follows on the stated interval.

Forward: T maps height, in meters, to temperature, in degrees Celsius. Inverse: T⁻¹ maps temperature θ, in degrees Celsius, to several possible heights, in meters. One-to-one behavior does not provide uniqueness.

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\(T(h)\) gives temperature in degrees Celsius at height \(h\) meters on an interval where \(T\) is one-to-one. Describe the forward and inverse mappings with units, and explain the uniqueness condition.

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