a. Let be a function whose domain is symmetric about the origin, that is, -x belongs to the domain whenever x does. Show that

a. Let ƒ be a function whose domain is symmetric about the origin, that is, -x belongs to the domain whenever x does. Show that ƒ is the sum of an even function and an odd function: ƒ(x) = E(x) + O(x), where E is an even function and O is an odd function.

b. Show that there is only one way to write ƒ as the sum of an even and an odd function.