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August 28th, 2012, 08:40 PM   #1
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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.
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August 28th, 2012, 08:48 PM   #2
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Re: Is this a rational function?

It is not a rational function by definition, since the denominator is not a polynomial function.
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August 28th, 2012, 08:50 PM   #3
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Re: Is this a rational function?

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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?
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August 28th, 2012, 08:53 PM   #4
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Re: Is this a rational function?

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Originally Posted by maxgeo
So exponents must be integers?
Yes, I believe.
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August 28th, 2012, 08:54 PM   #5
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Re: Is this a rational function?

Yes, although typically they are non-negative integers.
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August 28th, 2012, 08:58 PM   #6
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Re: Is this a rational function?

which is rational.

So, it's not necessary that the exponents must be non-negative integers.
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August 28th, 2012, 09:02 PM   #7
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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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