(a)

Let  be the number of pounds of the commodity costing  per pound. Because there are  pounds total, the amount of the second commodity is .

The total cost is 

.

(b)

Find the inverse of the original function.

Interchange the variables  and .

Substitute .

The inverse of the function is .

In the inverse function ,  represents total cost and  represents number of pounds of the less expensive commodity.

(c) Domain of inverse function :

The total cost will be minimum if we buy  pounds of less expensive commodity.

Therefore, the minimum value of  is .

The total cost will be maximum if we buy  pounds of more expensive commodity.

Therefore, maximum value of  is .

Domain of inverse function is .

(d)

Number of pounds of less expensive commodity is  when .

.

(a) .

(b) The inverse function , where  represents total cost and  represents number of pounds of the less expensive commodity.

(c) Domain of inverse function is .

(d) .