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<math>f(-x)=f_{e}(-x)+f_{0}(-x)=f_{e}(x)-f_{0}(x)</math> | <math>f(-x)=f_{e}(-x)+f_{0}(-x)=f_{e}(x)-f_{0}(x)</math> | ||
| − | <math> | + | solve for <math>f_{e}(x)</math> and <math>f_{0}(x)</math> |
<math>f_{e}(x)= (f(x)+f(-x))/2</math> | <math>f_{e}(x)= (f(x)+f(-x))/2</math> | ||
<math>f_{0}(x)= (f(x)-f(-x))/2</math> | <math>f_{0}(x)= (f(x)-f(-x))/2</math> | ||
Revision as of 07:42, 6 October 2008
a)
g(x)+h(x)=0
g(x) even h(x) odd
g is both even and odd
g(x)=g(-x)=-g(x)
b)
$ f(x)=f_{e}(x)+f_{0}(x) $
$ f(-x)=f_{e}(-x)+f_{0}(-x)=f_{e}(x)-f_{0}(x) $
solve for $ f_{e}(x) $ and $ f_{0}(x) $
$ f_{e}(x)= (f(x)+f(-x))/2 $
$ f_{0}(x)= (f(x)-f(-x))/2 $
