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b) | b) | ||
| − | f(x)=f$_{e}$(x)+f$_{0}$(x) | + | <math>f(x)=f$_{e}$(x)+f$_{0}$(x)</math> |
| − | f(-x)=f$_{e}$(-x)+f$_{0}$(-x)=f$_{e}$(x)-f$_{0}$(x) | + | <math>f(-x)=f$_{e}$(-x)+f$_{0}$(-x)=f$_{e}$(x)-f$_{0}$(x)</math> |
| − | solve for f$_{e}$(x) and f$_{0}$(x) | + | <math>solve for f$_{e}$(x) and f$_{0}$(x)</math> |
| − | f$_{e}$(x)= (f(x)+f(-x))/2 | + | <math>f$_{e}$(x)= (f(x)+f(-x))/2</math> |
| − | f$_{0}$(x)= (f(x)-f(-x))/2 | + | <math>f$_{0}$(x)= (f(x)-f(-x))/2</math> |
Revision as of 07:41, 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 $
