Inverse function

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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]

Examples[change | change source]

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[change | change source]

References[change | change source]

  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.