A reversible heat pump is a climate-control system that is an air conditioner and a heater in a single device. Operated in one direction, it pumps heat out of a house to provide cooling. Operating in reverse, it pumps heat into the building from the outside, even in cool weather, to provide heating. As a heater, a heat pump is several times more efficient than conventional electrical resistance heating. If some physical machines can run in two directions, we might ask whether some of the function “machines” we have been studying can also run backwards. In this topic, we will consider the reverse nature of functions.
- Verify inverse functions.
- Determine the domain and range of an inverse function
- Restrict the domain of a function to make it one-to-one.
- Find or evaluate the inverse of a function (including linear and composite functions).
- Use the graph of a one-to-one function to graph its inverse function on the same axes.