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August 28th, 2012, 08:40 PM  #1 
Member Joined: Mar 2012 Posts: 60 Thanks: 0  Is this a rational function?
Is 1/(x)^1/2 , or 1/sqroot(x) a rational function? I think it is a rational, but the text I am reading uses it as an example of what is not rational.

August 28th, 2012, 08:48 PM  #2 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,155 Thanks: 464 Math Focus: Calculus/ODEs  Re: Is this a rational function?
It is not a rational function by definition, since the denominator is not a polynomial function.

August 28th, 2012, 08:50 PM  #3  
Member Joined: Mar 2012 Posts: 60 Thanks: 0  Re: Is this a rational function? Quote:
 
August 28th, 2012, 08:53 PM  #4  
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  Re: Is this a rational function? Quote:
 
August 28th, 2012, 08:54 PM  #5 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,155 Thanks: 464 Math Focus: Calculus/ODEs  Re: Is this a rational function?
Yes, although typically they are nonnegative integers.

August 28th, 2012, 08:58 PM  #6 
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  Re: Is this a rational function? which is rational. So, it's not necessary that the exponents must be nonnegative integers. 
August 28th, 2012, 09:02 PM  #7 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,155 Thanks: 464 Math Focus: Calculus/ODEs  Re: Is this a rational function?
Yes, if given with negative exponents, it may be rewritten with nonnegative exponents. I just meant they are typically given as nonnegative, but not necessarily.


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