## Inverse functions

A function  is called a one-to-one function if it satisfies

whenever

The above condition becomes equivalent to the following:  always implies .'' When a function  is a one-to-one function, the inverse function  can be defined as the function satisfying

if and only if

We denote the inverse function of  by the symbol .

Domain of . If is a one-to-one function from the domain  to the range , then the inverse function  becomes a one-to-one function from the domain  to the range .

Department of Mathematics