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September 7th, 2009, 11:23 AM  #1 
Newbie Joined: Jul 2009 Posts: 11 Thanks: 0  Demonstration (symmetry)
Demonstrate that if x=a axis of symmetry for f(x) then: xfrom R. 
September 7th, 2009, 11:59 AM  #2 
Member Joined: Jul 2009 Posts: 34 Thanks: 0  Re: Demonstration (symmetry)
If x and y have the same distance from a and , then , and then from we get , so we get In the same way, if , then , and then too from we get again , so we get The last option that we have , and then it's obvious that 
September 9th, 2009, 09:15 PM  #3 
Global Moderator Joined: Dec 2006 Posts: 20,927 Thanks: 2205 
Too longwinded! By definition of symmetry, f(a  t) = f(a + t) for all real values of t. Putting t = a  x gives f(x) = f(2a  x) for all real values of x. 

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