A ball is attached to one end of a wire, the other end being fastened to the ceiling. The wire is held horizontal, and the ball is released from rest. It swings downward and strikes a block initially at rest on a horizontal frictionless surface. Air resistance is negligible, and the collision is elastic. The masses of the ball and block are, respectively, 1.48 kg and 2.77 kg, and the length of the wire is 1.11 m. Find the velocity of the ball just after the collision.

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 .

myth. it was once thought that animals, including cats and dogs, could only see in black and white. however, scientists have proven this to be a myth. in all animals, including humans, the perception of colour is determined by the presence of cells in the eye called cone photoreceptors.