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December 18th, 2012, 08:37 AM  #1 
Newbie Joined: Dec 2012 Posts: 23 Thanks: 0  prove there exists an inverse function
I'm quite new to calculus and frankly speaking I'm studying it on my own. Could you tell me how to solve this: Prove that there exists an inverese of . In what set is differentiable? Calculate I would really appreciate a thorough explanation. Thank you. 
December 18th, 2012, 08:57 AM  #2 
Math Team Joined: Sep 2007 Posts: 2,409 Thanks: 6  Re: prove there exists an inverse function
Okay, do you remember the requirements that a function be invertible? In order that for any given y we be able to find the x such that y= f(x), there must be at least one such x (f is "onto") and there must be just one such x (f is "onetoone"). Neither of those is true for sin(x) itself there is NO x such that sin(x)= 2 and there exist infinitely many x such that sin(x)= 0. I would suggest starting by looking at graph of .


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