(New page: 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$_{0}$...) |
|||
| Line 1: | Line 1: | ||
a) | a) | ||
| + | |||
g(x)+h(x)=0 | g(x)+h(x)=0 | ||
| + | |||
g(x) even h(x) odd | g(x) even h(x) odd | ||
| + | |||
g is both even and odd | g is both even and odd | ||
| + | |||
g(x)=g(-x)=-g(x) | g(x)=g(-x)=-g(x) | ||
| + | |||
b) | b) | ||
| + | |||
f(x)=f$_{e}$(x)+f$_{0}$(x) | f(x)=f$_{e}$(x)+f$_{0}$(x) | ||
| + | |||
f(-x)=f$_{e}$(-x)+f$_{0}$(-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) | solve for f$_{e}$(x) and f$_{0}$(x) | ||
| + | |||
f$_{e}$(x)= (f(x)+f(-x))/2 | f$_{e}$(x)= (f(x)+f(-x))/2 | ||
| + | |||
f$_{0}$(x)= (f(x)-f(-x))/2 | f$_{0}$(x)= (f(x)-f(-x))/2 | ||
Revision as of 07:40, 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
