Finding the Domain and the Range of Inverse Functions

General Mathematics / Functions and Their Graphs

Sample Question

Which of the following statements is not always true?

  • The domain of a one-to-one function [% f(x) %] is the range of its inverse function [% f^{-1}(x). %]
  • The range of a one-to-one function [% f(x) %] is the domain of inverse function [% f^{-1}(x). %]
  • If function [% g(x) %] is the inverse of the function [% f(x) %], then it must also be true that the function [% f(x) %] is the inverse of the function [% g(x). %]
  • If a point [% \left(x,y\right) %] is on the graph of function [% f(x) %], then the same point lies on the graph of its inverse function [% f^{-1}(x). %]

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