The ball's velocity will be represented by the derivative of its distance function:

Now find the times

for which this is equal to 30, i.e. solve

This has two solutions,

, but only one is positive and falls in the interval
![[0,3]](https://tex.z-dn.net/?f=%5B0%2C3%5D)
. So the velocity reaches 30 cm/s when

.
F(x) and g(x) were inverse functions, then if f(a) = b, then g(b) = a
f(x) = (5x+1) / x g(x) = x / (5x+1)
f(1) = 6, but g(6) = 6/31 ≠ 1
So, f(x) and g(x) are NOT inverse functions.
If I am correct the answer is 369,600 feet per hour.