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?
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$f(x)$ 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.
answered Apr 24, 2016 at 23:57