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November 17th, 2013, 08:59 AM  #1 
Newbie Joined: Nov 2013 Posts: 6 Thanks: 0  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)=2x (v) f(x)(x+3)^25 (vi) f(x)=x^2+4x+1 
November 17th, 2013, 09:37 AM  #2 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  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?

November 17th, 2013, 09:58 AM  #3 
Newbie Joined: Nov 2013 Posts: 6 Thanks: 0  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

November 17th, 2013, 11:12 AM  #4 
Senior Member Joined: Jun 2013 From: London, England Posts: 1,316 Thanks: 116  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.

November 17th, 2013, 11:31 AM  #5 
Newbie Joined: Nov 2013 Posts: 6 Thanks: 0  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(r1)^2]?? in terms of n Hence ,or otherwise ,evaluate ?_(r=51)^100??[r^2(r1)^2 ? 
November 17th, 2013, 01:47 PM  #6 
Math Team Joined: Sep 2007 Posts: 2,409 Thanks: 6  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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