Combination of even and odd functions Can someone help me how to show that any function $f(x)$ defined on a symmetrically placed interval can be written as a sum of an even and a odd function? 
What is the special role played by "symmetrically placed interval" here?

$f(x)$ can be written as the sum of $\frac{f(x)+f(-x)}{2}$, which is even, and $\frac{f(x)-f(-x)}{2}$, which is odd. The symmetric interval ensures that these functions are defined.
