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ravi623
 3 years ago
show that there is only one way to write f as the sum of an even function and an odd function
ravi623
 3 years ago
show that there is only one way to write f as the sum of an even function and an odd function

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satellite73
 3 years ago
Best ResponseYou've already chosen the best response.1one way is \[\frac{f(x)+f(x)}{2}+\frac{f(x)f(x)}{2}\] oh only one way...

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.1usual 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 \(o(x)=\frac{f(x)f(x)}{2}\)

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.1yes, that should work let me know if it is not clear

ravi623
 3 years ago
Best ResponseYou've already chosen the best response.0nice explanation, thanks!!
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