I know that to find the height of a woman that has a tibia bone measuring 43.4 would be computed like this

Question

H(t)=0.984(t)+28.6, and I would arrive at this :69.5696, but I how would I prepare a function to figure out a womeans tibia in inches when she is 5 foot, 5 inches. I am stuck.

Answer 1

I believe the formula should be something like:
H(t)=2.45t+28.6,
where t=tibia length measured in inches
28.6=constant in inches.
The formula varies with the race of the individual (the given one is for negroid female, in inches), and the original formula was for measurements in centimeters (1"=2.54 cm). The 28.6 came from a conversion from (72.56) cm to inches, but the factor 2.45 was probably inadvertently divided by 2.54 also.
See:
http://www.pbs.org/saf/1203/teaching/teaching2.htm

Now to answer the question, if
H(t)=mt+b, where m and b are constants, and t the independent variable representing the length of the tibia bone, we look for the inverse of the function H(t) such that
H^-1(h)=T(h)=ph+q where
p and q are constants derived from m and b, and T(h) is the tibia bone length, and h=body height.

To find the inverse of a function, we follow the following steps:
Let
h=H(t)=mt+b
solve t in terms of m, b, and h:
t=(h-b)/m
=(1/m)h - b/m
Therefore
T(h)=(1/m)h - b/m

For the given constants,
m=2.45, b=28.6, we get
T(h)=0.408h-11.67

For example, if the tibia bones measures 15", then
body height, h
= H(15)
= 2.45*15 + 28.6"
=65.4"

The inverse function is T(h), for a height of h=65.4,
T(65.4)=0.408*65.4-11.67
=15.0".