The inverse notation f−1 used a pure mathematics problem is not always used when finding inverses of applied problems. Rether, the inverse of a function such as C=C(q) will be q=q(C). The following problem illustrates this ideal. The ideal body weight W for men (in kilograms) as a function of height h (in inches) is given by the following functions. 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 cheking that W(n(W))=W=h c) What is the height of a male who is at his ideal weight of 80 killograms?

Question

The inverse notation f−1 used a pure mathematics problem is not always used when finding inverses of applied problems. Rether, the inverse of a function such as C=C(q) will be q=q(C). The following problem illustrates this ideal.  The ideal body weight W for men (in kilograms) as a function of height h (in inches) is given by the following functions.  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 cheking that W(n(W))=W=h  c) What is the height of a male who is at his ideal weight of 80 killograms?

Nathaniel Kramer · Accepted Answer

Step 1 The ideal body weight for men(in kilograms) as a function of height h (in inches ) is given by 1) W(h)=51+2.3(h−59) Step 2 a) Ideal weight for 6 foot men h=6foot=6×12 h=72inches put h=72 inches in equation (1) W(h)=51+2.3(h−59) W(72)=51+2.3(72−59) W(72)=51+2.3(13) W(72)=80.9 kilograms Ideal weight for 6 foot men =80.9 kilograms Step 3 b) Express the height h as a function of weight W=51+2.3(h−59) h−59=W−512.3 h=W−512.3+59 ⇒h(W)=W−512.3+59 W(h)=51+2.3(h−59) h(W)=W−512.3+59 Now for verification W(h(W)) W(h)=51+2.3(h−59) W(h(W))=51+2.3(W−512.3+59−59) W(h(W))=51+2.3(W−512.3) W(h(W))=51+W−51 W(h(W))=W and h(W(h)) h(W)=W−512.3+59 h(W(h))=51+2.3(h−59)−512.3+59 h(W(h))=h−59+59 h(W(h))=h W(h(W))=W and h(W(h))=h Hence proved Step 4 c) Find height of the male whose weight is 80 kilograms From the height function h(W)=W−512.3+59

The inverse notation f^{-1} used a pure mathematics problem is not always

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