The nuclei of carbon atoms that are found in nature come in two main “varieties” called isotopes (more on this in chapter 11). the carbon-14 nuclei have a greater mass than the carbon-12 nuclei. the two types of atoms can be separated from each other by ionizing them, accelerating them all to some uniform velocity, and then passing them between the poles of a magnet. why does this separate the two isotopes? describe the motion of the two ion types after passing out of the magnetic field. what would happen if all the atoms did not have the same speed?

they would not split from the nuclei if they were not going the same speed

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 .