Answer
Any function $f$ can be written as $$f(x)=\frac{1}{2} (f(x)+f(-x)) + \frac{1}{2} (f(x)-f(-x)),$$where the first term is even and the second term is odd.
Work Step by Step
Any function $f$ can be written as $$f(x)=\frac{1}{2} (f(x)+f(-x)) + \frac{1}{2} (f(x)-f(-x)).$$
The function $g(x)=\frac{1}{2}(f(x)+f(-x))$ is even since$$g(-x)=\frac{1}{2}(f(-x)+f(-(-x)))=\frac{1}{2}(f(x)+f(-x))=g(x),$$and the function $h(x)=\frac{1}{2} (f(x)-f(-x))$ is odd since$$h(-x)=\frac{1}{2} (f(-x)-f(-(-x)))=\frac{1}{2} (f(-x)-f(x))=-h(-x).$$
