Question 82614: re-writing my previous question, format didn't come out the way it was supposed to look like:
a) show that if f is any function, then the function E defined by:
E(x)= [(f(x)+f(-x))/2]is even
b) show that if f is any function, then the function O defined by
O(x)= [(f(x)-f(-x))/2] is odd
i hope the parenthetical notation is correct. basically, the functions E(x) and O(x) have f(x)adding or subtracting f(-x) and the sum or difference is then divided by 2.
thanks, sorry about the confusion, the first time i posted i tried to get fancy with the formatting, it didn't work i hope this one makes sense
Answer by kev82(151)   (Show Source):
You can put this solution on YOUR website! Hi,
This is simply a case of using one of the definitions of even and odd. A function E(x) is even if E(-x)=E(x), and a function O(x) is odd if O(-x)=-O(x).
I'll do the even one, hopefully you can do the odd one on your own.
=\frac{f(-x)+f(x)}{2}=\frac{f(x)+f(-x)}{2}=E(x))
See if you can do the same thing for the odd one.
Hope that helps,
Kev
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