Even functions $f$ are symmetric across the $y$-axis, meaning $f(-x)=f(x)$. Odd functions $g$ are symmetric across the origin, meaning $g(-x)=-g(x)$. As long as the domain of a function is symmetric across $0$ on the real line, it turns out that the function can be uniquely written as a sum of an even function and an odd function. We address this classic exercise here.
