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(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) .
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