Question

show that any function f(x) can be decomposed uniquely into a purely even part and a purely odd part\[f(x) = f_E(x) + f_O(x)\]

Answer 1

Hint: look at
\[ \frac{f(x) + f(-x)}{2} \]
and
\[ \frac{f(x) - f(-x)}{2} \]