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Continuous proofs

  1. Oct 31, 2007 #1
    say function f is continuous on (-[tex]\infty[/tex],[tex]\infty[/tex]). show that f can be written as f = g + h, where g is an even function and h is an odd function.

    help pleaseee!
  2. jcsd
  3. Oct 31, 2007 #2
    If f(x)=g(x)+h(x) where g is even and h is odd, then what is f(-x)?
  4. Oct 31, 2007 #3


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    yeah, use those properties to help you construct your g and h out of f's
  5. Oct 31, 2007 #4
    f(-x) = g(-x) + h(-x)
    f(-x) = g(x) - h(x)
    = g(x) + (-h(x))

    is that it??
  6. Oct 31, 2007 #5
    Ok, then what is f(x)+f(-x)? Then what is g(x), and finally what is h(x)?
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