What makes the box you made a "kinetic energy gauge"? In other words, explain in terms of energy conservation how knowing the coefficient of friction of your box would allow you to determine the kinetic energy of the ball at the bottom of the ramp, even if you did not know the mass of the ball.

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 .