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Problems with some work problems

  1. Sep 21, 2005 #1
    Hello

    I am having problems with two problems can somebody help me??

    1. Suppose g is a odd function and let h = f of g. Is h always an odd function? What if f is odd? what if f is even??

    2. Express the sufrace area of a cube as a function of the length of a side.

    thanks any help would be great

    P
     
  2. jcsd
  3. Sep 21, 2005 #2
    Both problems are straightforward cases of applying the definitions.
     
  4. Sep 21, 2005 #3
    What do you mean by applying the definitions?

    Thanks
     
  5. Sep 21, 2005 #4
    Write out the property that makes g an odd function in symbolic terms. See what it means with respect to h. Write out the property that f is an even/odd function. See what both mean with respect to h in symbolic terms by just plugging in all these definitions. Compare the behavior of h to the behavior of even and odd functions given in their definition.
     
  6. Sep 22, 2005 #5
    So if
    f of g with f being an odd function would result in h = f(g(-x)) = f(-x) = -x so function h would be odd or -h(x) = h(-x)

    and if was even it would result in h = f(g(-x)) = f(-x) = x so function h is even when f is even

    Is this correct???
     
  7. Sep 22, 2005 #6
    This line should read h = f(g(-x)) = f(-g(x)) if g is an odd function. We don't know that g(x)=-x, we just know that g(-x) = -g(x) if g is odd. If f is also an odd function, we get f(-g(x)) = -f(g(x)) = -h.
     
  8. Sep 22, 2005 #7
    thanks for the reply :)
     
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