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 January 19th, 2014, 07:33 PM #1 Newbie   Joined: Jan 2014 Posts: 19 Thanks: 0 Invertible Functions Determine whether f(x) = x^4 + 3x^3 +1 is invertible. f'(x) = 4x^3 + 9x^2 ... I'm not sure what to do next, or if that's even the way to begin solving. I'd really appreciate some help with this problem. January 19th, 2014, 09:49 PM #2 Math Team   Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,372 Thanks: 233 Re: Invertible Functions f(0) = 1 f(-3) = 1 So , we have two distinct values of x that produce the same value of y , therefore the function is not invertible. In other words , the point's (0 , 1) , (-3 , 1) are both on the graph so it definitely fails the horizontal line test there. Alternatively , any polynomial that has a positive even power of x will not be invertible. For this polynomial , the x^4 term makes it non-invertible  January 20th, 2014, 02:08 AM   #3
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Re: Invertible Functions

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 Originally Posted by agentredlum f(0) = 1 f(-3) = 1 So , we have two distinct values of x that produce the same value of y , therefore the function is not invertible. In other words , the point's (0 , 1) , (-3 , 1) are both on the graph so it definitely fails the horizontal line test there. Alternatively , any polynomial that has a positive even power of x will not be invertible. For this polynomial , the x^4 term makes it non-invertible Got it. Thank you very much. Tags functions, 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 Magnesium Linear Algebra 2 December 11th, 2013 02:09 AM soumita Linear Algebra 3 April 28th, 2013 04:49 PM shine123 Linear Algebra 1 September 21st, 2012 08:47 AM tinynerdi Linear Algebra 0 February 20th, 2010 05:58 PM 450081592 Linear Algebra 1 November 28th, 2009 01:32 AM

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