
Concept explainers
In applications, the symbols used for the independent and dependent variables are often based on common usage. So, rather than using to represent a function, an applied problem might use to represent the cost of manufacturing q units of a good. Because of this, the inverse notation used in a pure mathematics problem is not used when finding inverses of applied problems. Rather, the inverse of a function such as will be . So is a function that represents the cost as a function of the number of units manufactured, and is a function that represents the number as a function of the cost . Problems 91-94 illustrate this idea.
Ideal Body Weight One model for the ideal body weight for men (in kilograms) as a function of height (in inches) is given by the function
(a) What is the ideal weight of a 6-foot male?
(b) Express the height as a function of weight .
(c) Verify that is the inverse of by showing that and .
(d) What is the height of a male who is at his ideal weight of 80 kilograms?
[Note: The ideal body weight for women (in kilograms) as a function of height (in inches) is given by .

To find: One model for the ideal body weight for men (in kilograms) as a function of height (in inches) is given by the function.
a. What is the ideal weight of a 6-foot male?
Answer to Problem 91AYU
Solution:
For Men:
a. The ideal weight of a 6 – foot male is .
For Women:
a. The ideal weight of a 6 – foot female is .
Explanation of Solution
Given:
The ideal body weight for men as a height function.
Calculation:
a. Given the ideal weight of a 6-foot male.
i.e.,

To find: One model for the ideal body weight for men (in kilograms) as a function of height (in inches) is given by the function.
b. Express the height as a function of weight .
Answer to Problem 91AYU
Solution:
For Men:
b. The height as a function of weight .
For Women:
b. The height as a function of weight .
Explanation of Solution
Given:
The ideal body weight for men as a height function.
Calculation:
b. We can express as a function of weight .
Given .

To find: One model for the ideal body weight for men (in kilograms) as a function of height (in inches) is given by the function.
c. Verify that is the inverse of by showing that and .
Answer to Problem 91AYU
Solution:
For Men:
c. Verified that is the inverse of .
For Women:
c. Verified that is the inverse of .
Explanation of Solution
Given:
The ideal body weight for men as a height function.
Calculation:
c. Verify is the inverse of by showing below.
Similarly, we can prove

To find: One model for the ideal body weight for men (in kilograms) as a function of height (in inches) is given by the function.
d. What is the height of a male who is at his ideal weight of 80 kilograms? [Note: The ideal body weight for women (in kilograms) as a function of height (in inches) is given by ].
Answer to Problem 91AYU
Solution:
For Men:
d. .
For Women:
d. .
Explanation of Solution
Given:
The ideal body weight for men as a height function.
Calculation:
d. The height of a male who is at his ideal weight of 80 kilograms as.
We know that .
Given kilograms.
Therefore, .
.
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Precalculus
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