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

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

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

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

ravi623 Group TitleBest ResponseYou've already chosen the best response.0
nice explanation, thanks!!
 2 years ago
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