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November 17th, 2013, 08:59 AM   #1
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Find the range of each function f: R?R and say which ones

Hi guys,i REALLY need help this time, with these function and range, im not really understanding much about this

Find the range of each function f: R?R and say which ones are injective,surjective or bijective
(i) f(x) =2x
(ii) f(x)=x^2 +1
(iii) f(x)=1/x
(iv) f(x)=2-x
(v) f(x)(x+3)^2-5
(vi) f(x)=x^2+4x+1
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November 17th, 2013, 09:37 AM   #2
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Re: Find the range of each function f: R?R and say which o

Do you have specific troubles, or are you just looking for general resources on bijective/surjective/injective?
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November 17th, 2013, 09:58 AM   #3
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Re: Find the range of each function f: R?R and say which o

no, i have troubles on finding out what is the range of those above and i cant tell whether they are bijective,surjective or injective
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November 17th, 2013, 11:12 AM   #4
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Re: Find the range of each function f: R?R and say which o

Have you tried the first one? If you know what those terms mean, then it should be quite easy. Especially finding the range.
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November 17th, 2013, 11:31 AM   #5
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Re: Find the range of each function f: R?R and say which o

no i cant, i attempted it but it didnt work
i dont know where to start

and then i have this problem with the sigma notation
Given that ?_(r=1)^n??r=n(n+1)/2 ,express ?_(r=1)^n??[r^2-(r-1)^2]?? in terms of n
Hence ,or otherwise ,evaluate ?_(r=51)^100??[r^2-(r-1)^2 ?
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November 17th, 2013, 01:47 PM   #6
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Re: Find the range of each function f: R?R and say which o

Well, how about telling us what you are using as the definitions of "injective", "surjective" and "bijective". That might help us to help you.
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