Let the following functions be defined on the symmetric interval (- A, a) odd and even functions (1) The sum of two even functions is even and the sum of two odd functions is odd (2) Any function defined on a symmetric interval (- A, a) can be expressed as the sum of an odd function and an even function

Let the following functions be defined on the symmetric interval (- A, a) odd and even functions (1) The sum of two even functions is even and the sum of two odd functions is odd (2) Any function defined on a symmetric interval (- A, a) can be expressed as the sum of an odd function and an even function

Let f (x) and G (x) be even functions, m (x) be their sum function, and B be any point in the interval
F（b）=F（-b）,G（b）=G（-b）
M (x) = f (x) + G (x): m (b) = f (b) + G (b) = f (- b) + G (- b) = m (- b), so even function sum or even function, we can also prove that odd function sum is odd function