Question

Inverse notation f^-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 C= C(q) will be q= q(C). The following problem illustrates this idea.

The ideal body weight W for men (in kilograms) as a function of height h (m inches) is given by the following function.

W(h)= 49+2.2(h-60)

Required:
a. What is the ideal weight of a 6-foot male?
b. Express the height h as a function of weight W. Verify your answer by checking that W(h(W)) = W and h(W(h))h.

Answer 1

a) 75.4 kg

b)
`h(W)=(W+83)/(2.2)`

Explanation:

a) The ideal weight of a 6-foot (72 inches) male is given by simply applying h= 72 in to the expression:

`W(72) = 49+2.2(72-60)\\W(72) =75.4\ kg`

b) Expressing height as a function of weight:

`W(h)= 49+2.2(h-60)\\2.2h-132+49=W\\h(W)=(W+83)/(2.2)`

Verifying with W(h(W)):

`W(h(W))= 49+2.2((W+83)/(2.2) -60)\\W(h(W))= 49-132+W+83\\W(h(W))=W`

Verifying with h(W(h):

`h(W(h))=((49+2.2(h-60))+83)/(2.2)\\h(W(h))=((49+2.2h-132+83))/(2.2)\\h(W(h))=h`