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 noninvertible 
January 20th, 2014, 02:08 AM  #3  
Newbie Joined: Jan 2014 Posts: 19 Thanks: 0  Re: Invertible Functions Quote:
 

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