I have a function that describes a ball being thrown at an initial velocity of 192 ft/s, given by:

f(t) = 192t - 16t^2

I need to find an inverse function that yields the time 't' when the ball is at a height 'h' as the object travels upward:

t = 6 - [sqrt(576 - h) / 4]

Also, I need to find an inverse function that yields the time 't' when the ball is at height 'h' as the object travels downward:

t = 6 + [sqrt(576 - h) / 4]

The problem is that I can't figure out how to find these inverse functions fromf(t) = 192t - 16t^2. I tried factoring, but didn't have any luck. Also, since this is a second order function, it's not one-to-one, which means that it shouldn't have an inverse, right (since it will fail the horizontal line test)? The two answers that were given above were what was listed, but I can't figure out how to get to the answer.

Help would be greatly appreciated! Thanks!