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 April 12th, 2012, 06:35 PM #1 Senior Member   Joined: Apr 2012 Posts: 112 Thanks: 0 Number theory and finding the domain and range! Hi I have three questions, two on number theory and the other on finding range and domain. 1.) Find the largest domain possible for the function f(x)-> (2)/(2x^2 -6x+5) and find the range corresponding to this domain. I would like to know, is there any easy, shortcut method to do this? I have tried, it took a long time and my answer came out incorrect. What I did was to manually sub in numbers for x and then derive a conclusion from there. It is tedious and I am aware that I cant do this in an exam. How would you solve it? 2.) a,b and c are consecutive terms of both an AP and GP. Therefore a=b=c I don't understand why a=b=c. Surely the value must increase or decrease from a to c? Unless they're talking about the difference, but I don't see that in the question. 3.) 1+((3/2)x)+((3/2)x)^2+((3/2)x)^3+... I know that the common ratio is r=(3/2)x The question asks, write down the range of values for x for the series to converge. The answer was -10, is that right? Thank you so much! April 12th, 2012, 07:08 PM   #2
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Re: Number theory and finding the domain and range!

1.) Equate the denominator to zero to find what values (if any) to exclude from the set of reals for the domain:

Thus, we find no real numbers to exclude. Thus the domain is:

Now to find the range, the function will have its maximal value when the denominator is at its minimum, which will occur at the axis of symmetry:

At this value of x the denominator is and thus

Since the function has a horizontal asymptote of , the range is then:

[attachment=0:44r3687v]range.jpg[/attachment:44r3687v]

2.) For a, b and c to be consecutive terms in an arithmetic progression, we require:

For a, b and c to be consecutive terms in a geometric progression, we require:

Thus, we have:

Hence:

3.) Check out this article on the condition for convergence:

http://en.wikipedia.org/wiki/Geometric_series
Attached Images range.jpg (9.7 KB, 121 views) April 12th, 2012, 08:41 PM #3 Senior Member   Joined: Apr 2012 Posts: 112 Thanks: 0 Re: Number theory and finding the domain and range! Thank you so much!!  Tags domain, finding, number, range, theory Search tags for this page
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# the shortest method on how to find the domain and range of a function

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