A star-forming cloud flattens into a disk that spins faster as the cloud contracts because of conservation of angular momentum. Then material from the disk gradually spirals inward toward the newly forming star at the center, accreting onto its surface and adding to its mass. What would we find if we could measure the orbital speeds of gas particles in the accretion disk

v=ir = 3x15 =45 v

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 .