The 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 (in inches) is given by the following function. W(h) = 49 + 2.2(h- 60) What is the ideal weight of a 6-foot male? The ideal weight, W, of a 6-foot male is kilograms. (Round to the nearest tenth as needed.) 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 with Step-by-step explanation:Since we have given that [tex]W(h)=49+2.2(h-60)[/tex]if the height of male = 6 foot 1 foot = 12 inches6 foot = 72 inchesSo, the ideal weight would be [tex]W(6)=49+2.2(72-60)\\\\W(6)=49+2.2\times 12\\\\W(6)=75.4\ kg[/tex]Now,  Express the height h as a function of weight W.[tex]w=49+2.2(h-60)\\\\w-49=2.2(h-60)\\\\\dfrac{w-49}{2.2}=h-60\\\\\dfrac{w-49}{2.2}+60=h(W)[/tex]Now, W(h(W) ) is given by[tex]W(h(W))=49+2.2(\dfrac{w-49}{2.2}+60-60)\\\\W(h(W))=49+w-49\\\\W(h(W)=w[/tex]Similarly,[tex]h(W(h))=\dfrac{49+2.2(h-60)-49}{2.2}+60\\\\h(W(h))=\dfrac{2.2(h-60)}{2.2}+60\\\\h(W(h))=h-60+60\\\\h(W(h))=h[/tex]