Two charged conducting spheres have net charges of +4 μC and -8 μC and attract each other with a force of 16 mN. The spheres are brought into contact and then moved apart to the initial distance. What is the new force between the spheres? Is this force attractive or repulsive?

thermal energy is the answer

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 .