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 April 9th, 2013, 03:05 PM #1 Newbie   Joined: Apr 2013 Posts: 7 Thanks: 0 Find all linear function given a function equals its inverse Hello, I'm not sure exactly what I need to do for the following question - Find all linear functions f(x) = ax + b such that f(x) = f^-1 (x), where f(x) = (x - 3)^2(4 - x)(2x + 1) Anyone able to give me a clue where to start? Thank you, April 9th, 2013, 05:52 PM #2 Global Moderator   Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,958 Thanks: 1146 Math Focus: Elementary mathematics and beyond Re: Find all linear function given a function equals its inv You have conflicting definitions for f(x) and (x - 3)^2(4 - x)(2x + 1) is not invertible over the domain of real numbers. Is this exactly how the problem appears? April 10th, 2013, 01:59 AM #3 Newbie   Joined: Apr 2013 Posts: 7 Thanks: 0 Re: Find all linear function given a function equals its inv 'Find all linear functions f(x) = ax + b such that f(x) = f^-1(x)" is how the question appears. (x-3)^2(4-x)(2x+1) is defined in a previous question and I thought it carried over into this one, but I'm probably wrong. I had assumed F(x) = ax + b was just the form of the linear function I was to attempt to find. April 10th, 2013, 06:09 AM #4 Math Team   Joined: Sep 2007 Posts: 2,409 Thanks: 6 Re: Find all linear function given a function equals its inv Yes, any linear equation can be written as f(x)= y= ax+ b. To find such functions that satisfy , you need, certainly, first to find the inverse function! You can do that by "swapping" y and x: solve x= ay+ b for y, then set the two equal. Being equal, for functions, means equal for all x so choosing two different values of x will give you two equations to solve for a and b. Of course, the problem says "find all linear functions" so you cannot find specific values for a and b. April 10th, 2013, 01:17 PM #5 Global Moderator   Joined: Dec 2006 Posts: 20,937 Thanks: 2210 As f(x) is its own inverse, f(f(x)) = x, so a�x + ab + b = x. Hence a� = 1. If a = 1, b must be 0 and f(x) = x. If a = -1, b can have any value and f(x) = -x + b. Tags equals, find, function, inverse, linear Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post alyssa jesse Algebra 2 September 14th, 2013 03:35 PM mike++ Algebra 2 July 25th, 2013 02:14 PM junsugal Linear Algebra 0 March 4th, 2012 09:40 PM jaredbeach Algebra 1 November 17th, 2011 11:58 AM sivela Calculus 1 February 8th, 2011 01:43 PM

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