We analyse data from two studies in Ireland and Sweden relating to the concept of inverse function. In particular, we consider components of the participants’ evoked concept images of this topic when answering open questionnaire questions. The results show that the students’ concept images contain algebraic, geometric and more formal components: both Irish and Swedish students describe inverse functions as swapping x and y, as a reflection or a reversal. How various components may or may not enrich students’ conceptual understanding of inverse functions is discussed.