Question

A penny drops from a building 45 feet above the ground. The function h(t) = - 16t²+45 gives the height to the penny after t seconds.

(A )Based on the problem situation, what are the domain and range of h(t) the domain and range of inverse of h(t).
(B) Based on the problem situation, write a function for h-¹(t). What does this function represent in terms of the problem situation?

Answer 1

See below.

Explanation:

h(t) = - 16t²+45

This equation tells us the height of the penny, h(t), in feet, as a function of time, t, in seconds. The 45 is telling us that the height of the penny when dropped (at t = 0) is 45 feet. It also tells us that the penny accelerates at -16 feet/sec^2. The minus says it is headed towards Earth, which is the definition of 0 feet (ground level).

(A). The domain is time, t, from 0 to however many seconds it takes to reach the ground.

(B). An inverse function will undo the action of the another function.

This means that whenever y=f(x) then x=g(y). Applying f first and then g is the same thing as doing nothing.

That said, the inverse of h(t) = - 16t²+45 is unknown to me. Sorry.