Inverse Functions


Introduction to Sets Show

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Injections, Surjections, and Bijections Show

Inverse Functions


  • If f is a function, then its inverse function g is defined as the reverse of the mapping created by f.
  • If g is an inverse of f then:
  • and:


  • To find the inverse of a function given as an equation, we can simply solve for y


To denote that a function is an inverse of another, two different notations are commonly used:
  • If the function is representedby the letter f then its inverse is can be denoted using a superscript of -1
  • If the function is represented by the letter f then its inverse is can be denoted using the letter g


  • If the original function is a bijection then its inverse will also be a bijection.
  • If the original function is not a bijection then there is no guarantee that it has an inverse.
    • If it is not injective then there may be two elements in the domain that map to the same element in the codomain.
    • If it is not surjective then there may be an element in the codomain that is not mapped to from the domain.