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49

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PAGE: 344SET: ExercisesPROBLEM: 49
Please look in your text book for this problem Statement

(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 image and image.

Substitute .

The inverse of the function is .

In the inverse function , image represents total cost and image 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 image is .

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

Therefore, maximum value of image is .

Domain of inverse function is .

(d)

Number of pounds of less expensive commodity is image when .

.

(a) .

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

(c) Domain of inverse function is .

(d) .



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