anonymous
  • anonymous
show that there is only one way to write f as the sum of an even function and an odd function
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
one way is \[\frac{f(x)+f(-x)}{2}+\frac{f(x)-f(-x)}{2}\] oh only one way...
anonymous
  • anonymous
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 \(o(x)=\frac{f(x)-f(-x)}{2}\)
anonymous
  • anonymous
yes, that should work let me know if it is not clear

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anonymous
  • anonymous
nice explanation, thanks!!
anonymous
  • anonymous
yw

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