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 October 4th, 2012, 04:24 PM #1 Newbie   Joined: Sep 2012 Posts: 15 Thanks: 0 Let f be an invertible function, and g = f^-1.... Let 'f' be an invertible function, and g=f^-1. Find which of the following functions F is also invertible (explain, derive a formula for F^-1), or give a counter example (can be a graph) if not always so. (a) F(x)=2f(x-2); (b) F(x)=f^2(x); Can someone please walk me through the steps of answering this question? October 5th, 2012, 03:26 AM #2 Global Moderator   Joined: Dec 2006 Posts: 20,932 Thanks: 2207 (a) Inverse is g(x/2) + 2 (since F(g(x/2) + 2) = 2f(g(x/2)) = 2(x/2) = x). (b) Counterexample: f(x) = x�, g(x) = ?x, where x is real, since x^6 is not invertible (1^6 = (-1)^6). To obtain the answer for (a), I used the following steps, where G(x) is the inverse to be found (assuming it exists): x = 2f(G(x) - 2) f(G(x) - 2) = x/2 G(x) - 2 = g(x/2) G(x) = g(x/2) + 2. Tags function, invertible 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 soumita Linear Algebra 3 April 28th, 2013 04:49 PM shine123 Linear Algebra 1 September 21st, 2012 08:47 AM problem Linear Algebra 3 August 31st, 2011 05:30 AM tinynerdi Linear Algebra 0 February 20th, 2010 05:58 PM rbaptista Linear Algebra 1 November 23rd, 2008 01:58 PM

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