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## Homework Statement

a. Prove that any function f with domain R can be written f = E + O, where E is even and O is odd.

b. Prove that this way of writing f is unique.

## Homework Equations

## The Attempt at a Solution

Well, I didn't know where to start and I don't know where I'm trying to go, so I don't know if I'm even on the right track.

since even: f(x) = f(-x) and odd: f(x) = -f(-x) -- as well as f(-x) = -f(x)...

E(x) + O(x) = E (x) + O(x)

E(-x) + O(x) = E(x) + O(x)

E(-x) + O(-x) = E(x) - O(x)

(E+O)(-x) = (E-O)(x)

not sure where to go from here. so if someone could help me figure out what I'm trying to end up with? or where to go from here?I would very much appreciate it. thanks!