Hello wonderful mathematics people. This is Anna Cox from Kellogg Community College. 1 to one functions. If X1 and X2 are in the domain of the function, and X1 doesn't equal X2, then F of X1 doesn't equal F of X2. What it really means is every X has a unique Y and every Y has a unique X. To know if a relationship was a function, it had to pass a vertical line test, which meant every vertical line that we put on the graph could only pass through the graph one time. For something to be 1 to one, it also has to pass the horizontal line test, which says that any graph can only have passed through one time. For both a vertical line test and also for a horizontal line test, if it passes through more than once, it would not be a one to one function. If a function is 1 to one, then it has an inverse denoted by F inverse of X. The domain of F of X is the range of its inverse and the range of the original function is the domain of its inverse. Basically the X&Y switch places composition F inverse of F of X has to equal X where X is in the domain of F because X was the inner most with that F and also FF inverse of X has to equal X where X was in the domain of F Inverse F of X&F inverse of X are symmetric with respects to the line Y equal X. Thank you and have a wonderful day.