### Inverse Functions

Consider the function (f:x mapsto x – 2) with domain A = {1, 3, 4,7}. Then the range of the function is B = {-1, 1, 2, 5}. The arrow diagram representing this function is shown as below.

If the arrows of (a) are reversed, the arrow diagram in (b) is obtained. A new function having domain B and range A is formed from the function *f*. This new function is called the inverse function of f and is denoted by *f ^{-1}* .