My Math Forum Is a function's inverse always injective?
 User Name Remember Me? Password

 Real Analysis Real Analysis Math Forum

 January 29th, 2017, 09:53 AM #1 Member   Joined: Aug 2011 Posts: 42 Thanks: 0 Is a function's inverse always injective? Hey! Assume a function $\displaystyle f$ is defined, and we know that $\displaystyle f^{-1}(a)=x$ and $\displaystyle f^{-1}(b)=x$. Can we then say that $\displaystyle a=b$ because $\displaystyle f^{-1}$ has to be injective. I'm thinking that if $\displaystyle f^{-1}$ is not injective, then we would have problems defining $\displaystyle f$.
 January 29th, 2017, 10:03 AM #2 Senior Member     Joined: Sep 2015 From: USA Posts: 2,174 Thanks: 1143 if $f^{-1}$ isn't injective then $f$ isn't a function
 January 29th, 2017, 10:25 AM #3 Member   Joined: Aug 2011 Posts: 42 Thanks: 0 Right! That's what I suspected. Thanks for the clarification!
 February 4th, 2017, 05:30 PM #4 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,261 Thanks: 894 Note that not every function is invertible. The function itself has to be injective in order to have an inverse. And, of course, the function is itself the inverse of its inverse.

 Tags function, functions, injective, inverse

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post ach4124 Calculus 2 March 27th, 2015 06:37 PM Senna Real Analysis 2 June 27th, 2014 11:00 PM eraldcoil Abstract Algebra 3 April 24th, 2011 01:38 PM lime Real Analysis 2 July 29th, 2009 12:54 PM Powermonster Algebra 10 September 30th, 2008 06:51 AM

 Contact - Home - Forums - Cryptocurrency Forum - Top

Copyright © 2018 My Math Forum. All rights reserved.