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 August 28th, 2012, 07:40 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, 07:48 PM #2 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,184 Thanks: 481 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, 07:50 PM   #3
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Re: Is this a rational function?

Quote:
 Originally Posted by MarkFL It is not a rational function by definition, since the denominator is not a polynomial function.
So exponents must be integers?

August 28th, 2012, 07:53 PM   #4
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Re: Is this a rational function?

Quote:
 Originally Posted by maxgeo So exponents must be integers?
Yes, I believe.

 August 28th, 2012, 07:54 PM #5 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,184 Thanks: 481 Math Focus: Calculus/ODEs Re: Is this a rational function? Yes, although typically they are non-negative integers.
 August 28th, 2012, 07:58 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? $x^{-2}= \frac{1}{x^2}$ which is rational. So, it's not necessary that the exponents must be non-negative integers.
 August 28th, 2012, 08:02 PM #7 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,184 Thanks: 481 Math Focus: Calculus/ODEs Re: Is this a rational function? Yes, if given with negative exponents, it may be rewritten with non-negative exponents. I just meant they are typically given as non-negative, but not necessarily.

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