Posted by matt on Wednesday, November 26, 2008 at 12:59pm.
Suppose the following about a certain object:
I. The object's altitude is a function of time, represented by the function A(x) where here x is time.
II. The temperature of the object is a function of its velocity, represented by the function T(x), where here x is the object's velocity.
III. The weight of the object is a function of its altitude, represented by the function W(x), where here x is the object's altitude.
IV. The velocity of the object is a function of its weight, represented by the function V(x), where here x is the object's weight.
The function F(t) which gives us the object's temperature at time t can be represented as

calculus  Damon, Wednesday, November 26, 2008 at 1:26pm
To keep track of all that I need to use different variable labels that make more sense to me.
A(t)
T(v)
w(A)
v(w)
Now we want T(t)
T(v)= T(v(w))
but v(w) = v(w(A))
so
T(A) = T(v(w(A)))
but w(A) = w(A(t))
so
T(t) = T(v(w(A(t)))) which is our F(t)