Real Function is Expressible as Sum of Even Function and Odd Function/Examples

Examples of Use of Real Function is Expressible as Sum of Even Function and Odd Function

Let $f: \R \to \R$ denote the real function:

$\map f x = e^{2 x} \sin x$

$f$ can be expressed as the pointwise sum of:

the even function $\map g x = \dfrac {\paren {e^{2 x} - e^{-2 x} } \sin x} 2$

and:

the odd function $\map h x = \dfrac {\paren {e^{2 x} + e^{-2 x} } \sin x} 2$