In the last chapter, we looked at where points in the domain are mapped to under a function \(f: X \rightarrow Y\) and where points in the range come from under f. But sometimes we need to look at where f maps a whole set, or where an entire set comes from. This brings us to the notion of the image of a set under a function, and the inverse image of a set. We’ll collect the most important results on images and inverse images in the final theorem of the chapter. In the spotlight Minimum or Infimum, we discuss the Dirichlet problem, a problem that deals with trying to find solutions inside a ball (or disc) from function values on the sphere (or circle), and we use it to illustrate the importance of the difference between the minimum and the infimum.