Question

One model for the ideal body weight, W, for men (in kilograms) is W = 50 + 2.3(h-60), where h represents height (in inches).

1. According to this model, what is the ideal weight of a 6-foot male?
2. Rewrite the function in order to express height as a function of weight. Call this function h. Show your work.
3. Verify that the given function and your function from part (b) are inverses, by showing that (W°h)(W) = W and that (h°W)(h) = h.
4. What is the height of a male whose ideal weight is 83 kg?

Answer 1

1) Height of 6 foot male could be 77.6 kg.

2) Function of h as form of W,
`h=\Rightarrow (W+88)/(2.3)`

4) Height of a male would be 74.35 inches.

Explanation:

Ideal body weight model, W=50 + 2.3(h-60)

where, W is idea weight (in kilogram) and h represents height (in inches)

Part 1) We need to find ideal weight for 6 foot.

First we change 6 foot into inches

1 feet = 12 inch

6 foot = 72 inches

So, h=72 inches

Now we will put h=72 into W=50 + 2.3(h-60)

W=50 + 2.3(72-60)

W=77.6 Kg

Thus, Height of 6 foot male could be 77.6 kg.

Part 2) Rewrite the function as function of W

W=50 + 2.3(h-60)

2.3(h-60)=W-50

`h=(W-50)/(2.3)+60\Rightarrow (W+88)/(2.3)`

Thus, Function of h as form of W,
`h=\Rightarrow (W+88)/(2.3)`

Part 3) Verify (Woh)=h and (hoW)=h

(Woh)=
`50+2.3((W+88)/(2.3)-60)`

(Woh)=50+(W-50) = W

Similarly,

(hoW)=
`(50 + 2.3(h-60)-88)/(2.3)`

(hoW)=
`(50 +2.3h-50)/(2.3)\Rightarrow h`

Thus, Given function inverses to each other.

Part 4) Given
`h=(W-88)/(2.3)`

We need to find height of male of 83 kg weight. So, we put W=83 into above equation.

`h=(83+88)/(2.3)\Rightarrow 74.35\ inches.`

Thus, Height of a male would be 74.35 inches.