Chapter 5 - Logarithmic, Exponential, and Other Transcendental Functions - 5.3 Exercises - Page 344: 59

The inverse function will be a function in terms of the volume and gives the time taken for a certain volume of water to have passed through.

For g(t) to have an inverse function, it must be a 1-1 function. Since the volume of water that has passed through the water line cannot decrease over time, g(t) is a strictly increasing function. Hence, g(t) is 1-1 function and has an inverse. The inverse function will be a function in terms of the volume and gives the time taken for a certain volume of water to have passed through.