If P represents the pull of the wagon on the horse and the horse on the wagon, f represents the frictional force between the wagon wheels and the ground, and F represents the reaction force of the horse pushing against the ground, then the net force that accelerates the system is equal to

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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 .