Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

ravi623

  • 4 years ago

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

  • This Question is Open
  1. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    one way is \[\frac{f(x)+f(-x)}{2}+\frac{f(x)-f(-x)}{2}\] oh only one way...

  2. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    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 \(o(x)=\frac{f(x)-f(-x)}{2}\)

  3. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yes, that should work let me know if it is not clear

  4. ravi623
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    nice explanation, thanks!!

  5. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yw

  6. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy