The inverse notation fSuperscript negative 1 used in a pure mathematics problem is not always used when finding inverses of applied problems. ​ Rather, the inverse of a function such as Cequals​C(q) will be qequals​q(C).  The following problem illustrates this idea.
The ideal body weight W for men​ (in kilograms) as a function of height h​ (in inches) is given by the following function.
​W(h)equals50plus2.4​(hminus61​)
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Part 1
​(a)  What is the ideal weight of a​ 6-foot male?


To find the ideal weight of a 6-foot male using the given function \( W(h) = 50 + 2.4(h - 61) \), we first need to convert the height from feet to inches.

### Step 1: Convert height to inches
Since 1 foot equals 12 inches, a 6-foot male is:
\[
6 \text{ feet} \times 12 \text{ inches/foot} = 72 \text{ inches}
\]

### Step 2: Substitute \( h = 72 \) inches into the function
\[
W(72) = 50 + 2.4(72 - 61)
\]

### Step 3: Simplify the expression
\[
W(72) = 50 + 2.4 \times 11
\]
\[
W(72) = 50 + 26.4
\]
\[
W(72) = 76.4 \text{ kilograms}
\]

So, the ideal weight of a 6-foot male is **76.4 kilograms**.

Would you like a detailed explanation on how this formula was derived or have any questions? 

Here are some related questions for further exploration:

1. What is the ideal weight for a 5-foot-10-inch male using the same formula?
2. How would the formula change if the height was measured in centimeters instead of inches?
3. What is the inverse function of \( W(h) = 50 + 2.4(h - 61) \), and how can it be used to find height given a weight?
4. If a male's ideal weight is 85 kg, what is his height according to the formula?
5. How does the coefficient 2.4 in the function \( W(h) \) affect the relationship between height and weight?

**Tip:** When dealing with functions, always make sure to use consistent units (e.g., feet to inches) to avoid errors in calculations.

Learn how to calculate the ideal weight of a 6-foot male using the function W(h) = 50 + 2.4(h - 61). Step-by-step solution provided with conversions from feet to inches and detailed calculations. Suitable for high school students.

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