Inverse function

An inverse function is a concept of mathematics. A function will calculate some output , given some input . This is usually written . The inverse function does the reverse. Let's say  is the inverse function of , then . Or otherwise put, . An inverse function to  is usually called . It is not to be confused with , which is a reciprocal function.

Examples
If  over real , then 

To find the inverse function, swap the roles of  and  and solve for . For example,  would turn to , and then . This shows that the inverse function of  is .

Not all functions have inverse functions: for example, function  has none (because , and  cannot be both 1 and -1), but every binary relation has its own inverse relation.

In some cases, finding the inverse of a function can be very difficult to do.

Related pages
 Inverse element
 Inverse triangle function
 Inverse hyperbolic function
 Invertible matrix
 Reciprocal

 References 

Category:Functions and mappings
Category:Set theory