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.
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.