Is work done if you carry a book across the room at a constant velocity?

NO

Explanation:

As we know by work energy theorem that work done by all forces is given by change in kinetic energy of the system

it is given as

so here since the kinetic energy is constant for the system

so here change in kinetic energy is zero

hence the net work done must be zero

Here we know that

so here we can say that

so no work is required to move the books at constant speed from one position to other position

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 .