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

Dillard

Dillard

Answered question

2021-09-19

The inverse notation f1 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?

Answer & Explanation

Nathaniel Kramer

Nathaniel Kramer

Skilled2021-09-20Added 78 answers

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(h59)
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(h59)
W(72)=51+2.3(7259)
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(h59)
h59=W512.3
h=W512.3+59
h(W)=W512.3+59
W(h)=51+2.3(h59)
h(W)=W512.3+59
Now for verification
W(h(W))
W(h)=51+2.3(h59)
W(h(W))=51+2.3(W512.3+5959)
W(h(W))=51+2.3(W512.3)
W(h(W))=51+W51
W(h(W))=W
and
h(W(h))
h(W)=W512.3+59
h(W(h))=51+2.3(h59)512.3+59
h(W(h))=h59+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)=W512.3+59

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