Inverse function

function that "reverses" another function: if the function f applied to an input x gives a result of y, then applying its inverse function g to y gives the result x, and vice versa. i.e., f(x) = y if and only if g(y) = x

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 .[1] It is not to be confused with , which is a reciprocal function.[2]


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 pagesEdit


  1. "Comprehensive List of Algebra Symbols". Math Vault. 2020-03-25. Retrieved 2020-09-08.
  2. Weisstein, Eric W. "Inverse Function". Retrieved 2020-09-08.