If 10.0 J of work are required to transfer 2.00 coulombs of charge from point X to point Y in an electric field, what is the
difference in potential between these two points?

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 .

electric field is a function of 1/r^2

yes, the force per unit charge for a point charge is inverse square law.