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| Line 11: | Line 11: | ||
b) | b) | ||
| − | <math>f(x)= | + | <math>f(x)=f_{e}(x)+f_{0}(x)</math> |
| − | <math>f(-x)= | + | <math>f(-x)=f_{e}(-x)+f_{0}(-x)=f_{e}(x)-f_{0}(x)</math> |
| − | <math>solve for | + | <math>solve for f_{e}(x) and f_{0}(x)</math> |
| − | <math> | + | <math>f_{e}(x)= (f(x)+f(-x))/2</math> |
| − | <math> | + | <math>f_{0}(x)= (f(x)-f(-x))/2</math> |
Revision as of 08:42, 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 $
