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September 7th, 2009, 11:23 AM   #1
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Demonstration (symmetry)

Demonstrate that if x=a axis of symmetry for f(x) then:

x-from R.
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September 7th, 2009, 11:59 AM   #2
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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
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September 9th, 2009, 09:15 PM   #3
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Too long-winded!
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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