March 16th, 2009, 03:20 AM  #1 
Newbie Joined: Mar 2009 Posts: 20 Thanks: 0  Domains and composites.
Hi, For the function would the domain be any real number except 1, 2 and 11? I'm not sure if I expand the brackets out first or not. For the functions and are the composites; f.h = h.f = which would then result in both being ? And would the codomain be ? 
March 16th, 2009, 08:59 AM  #2 
Newbie Joined: Mar 2009 Posts: 21 Thanks: 0  Re: Domains and composites.
For the first function, the domain would be For the second problem: \mapsto x" /> \mapsto x" /> 
March 16th, 2009, 02:22 PM  #3 
Newbie Joined: Mar 2009 Posts: 20 Thanks: 0  Re: Domains and composites.
Not 11? Also, how did you get the first of the composites? 
March 16th, 2009, 05:25 PM  #4 
Senior Member Joined: Feb 2009 From: Adelaide, Australia Posts: 1,519 Thanks: 3  Re: Domains and composites.
Yes, 11. For h of f: first you square, then take the (positive) square root. Zero goes to zero, positive x goes to x, negative x goes to x (which is positive). For f of h: first you take the square root, then square. Zero goes to zero, positive x goes to x, negative x has no square root and so can't be in the domain. The codomain for both is all nonnegative real numbers. 
March 16th, 2009, 06:41 PM  #5 
Senior Member Joined: Dec 2008 Posts: 306 Thanks: 0  Re: Domains and composites.
Aswoods, you mean the range! You don't get to specify the codomain.

March 17th, 2009, 04:23 AM  #6 
Newbie Joined: Mar 2009 Posts: 21 Thanks: 0  Re: Domains and composites.
Good ol' codomain/range war =]


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