When you shuffle your feet across the carpet and then reach your hand to a nearby doorknob, you may create a spark between your hand and the door knob. Explain the Physics behind it in terms of electric potential difference. Explain well.

e/c, where e is its total 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 .