Here's the question you clicked on:
ravi623
show that there is only one way to write f as the sum of an even function and an odd function
one way is \[\frac{f(x)+f(-x)}{2}+\frac{f(x)-f(-x)}{2}\] oh only one way...
usual idea is to imagine there are are two ways and then show they are the same. so maybe put \[f(x)=e(x)+o(x)=\frac{f(x)+f(-x)}{2}+\frac{f(x)-f(-x)}{2}\] where \(o(x)\) is odd and \(e(x)\) is even and then show that \(e(x)=\frac{f(x)+f(-x)}{2}\) and \(o(x)=\frac{f(x)-f(-x)}{2}\)
yes, that should work let me know if it is not clear
nice explanation, thanks!!