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November 15th, 2009, 06:07 AM  #1 
Member Joined: Oct 2009 Posts: 59 Thanks: 0  Range of a function
Functions g and h are defined as follows: g : x ? 1 + x x ? R h : x ? x² + 2x x ? R Find i.) the ranges of g and h, range of g => R = {y : y ? R} 1 + x = 0 x = 1 1  2 = 1 b/2a = 2/2 = 1 range of h => R = {y : y ?  1, y ? R} ii.) the composite functions h o g and g o h, stating their ranges. Not sure how this is to be done help needed. 
November 15th, 2009, 07:31 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 20,629 Thanks: 2077 
The range of a function is the set of all values the function can have. It depends on the function's domain. Do you understand the term "domain"? For real x, 1 + x can have any real value, so its range is R, the set of all reals. For real x, since x² + 2x ?(x + 1)²  1, its range is all real values ? 1. The composite function g(h(x)) ?1 + x² + 2x ?(x + 1)², so its range is all real values ? 0. What progress can you make in finding the range of the composite function h(g(x))? 
November 15th, 2009, 08:47 AM  #3  
Member Joined: Oct 2009 Posts: 59 Thanks: 0  Re: Quote:
Represented mathematically it would be...R = {x : x ? R} R = {x : x ?  1, y ? R} What progress can you make in finding the range of the composite function h(g(x))? h{g(x)} ? h(1 + x) ? x² + 1 + 2(1 + x)² ? 3x² + 4x + 3.......I think?!  
November 15th, 2009, 09:59 AM  #4  
Global Moderator Joined: Dec 2006 Posts: 20,629 Thanks: 2077  Quote:
Quote:
Quote:
Can you obtain the range of this function?  
November 15th, 2009, 11:14 AM  #5  
Member Joined: Oct 2009 Posts: 59 Thanks: 0  Re: Quote:
 
November 15th, 2009, 09:49 PM  #6 
Senior Member Joined: Feb 2009 From: Adelaide, Australia Posts: 1,519 Thanks: 3  Re: Range of a function
I think h(x) has a minimum at x = 2.

November 16th, 2009, 12:40 AM  #7  
Member Joined: Oct 2009 Posts: 59 Thanks: 0  Re: Range of a function Quote:
 
November 16th, 2009, 01:41 AM  #8 
Senior Member Joined: Feb 2009 From: Adelaide, Australia Posts: 1,519 Thanks: 3  Re: Range of a function
The range will be [h(2), ?) because the range is the output of h, not the input. So it's [1, ?). By the way, are you supposed to use the convention of square brackets versus round brackets? So [1... includes 1, but (1... excludes it? 
November 24th, 2009, 01:50 PM  #9  
Member Joined: Oct 2009 Posts: 59 Thanks: 0  Re: Range of a function Quote:
I'm not sure. The teacher never said anything about round or square brackets, although he uses the round ones.  

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