Aroller coaster at an amusement park goes from the top of a tall hill to the bottom. during this time, the roller coaster

There are a couple of things happening while the coaster goes from the top of the hill to the bottom:

The roller coaster loses potential energy and gains kinetic energy.

we have been given a quadratic function and we need to restrict the domain such that it becomes a one to one function.

we know that vertex of this quadratic function occurs at (5,2).

further, we know that range of this function is .

if we restrict the domain of this function to either or , it will become one to one function.

let us know find its inverse.

upon interchanging x and y, we get:

let us now solve this function for y.

hence, the inverse function would be if we restrict the domain of original function to and the inverse function would be if we restrict the domain to .