An empirical study suggests that a brewerys weekly sales of

Question

Question: 1. An empirical study suggests that a brewery's weekly sales of beer are determined by the average air temperature given that the price of beer, income, adult population and most other variables are constant in the short run. This functional relationship is estimated as

X = 400 + 16T^0.5         for T^0.5 > 0

where X is the number of barrels sold per week and T is the mean average air temperature, in oF. What is the mathematical inverse of this function? Does it make sense to specify such an inverse function in economics?

2. Make up your own examples for:

(a) a function that has an inverse, and then derive the inverse function;

(b) a function that does not have an inverse and then explain why this is so.