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Simple question

  1. Sep 16, 2005 #1
    just starting up the school year again and my brain is not there yet.

    Is e^x an even or odd function.

    also what about
    e^x + e^-x

    and

    e^x - e^-x

    thanks for the help.
     
  2. jcsd
  3. Sep 16, 2005 #2

    shmoe

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    Have you tried to apply the definitions of even and odd functions? Where does it get you?
     
  4. Sep 16, 2005 #3
    it gets me nowhere. applying the definition and inserting -x into e^x just gives (1/e^x) which is neither f(x) nor -f(x).
     
  5. Sep 16, 2005 #4
    a function is even iff f(-x) = f(x), for example cos(x)
    a function is odd iff f(-x) = -f(x), for example sin(x)

    exp(-x) <> exp(x) <> -exp(x), so exp(x) is neither
    exp(-x)+exp(x) = exp(x)+exp(-x), so exp(x)+exp(-x) is even (=2cos(x))
    exp(-x)-exp(x) = -(exp(x)-exp(-x)), so exp(x)-exp(-x) is odd (=2isin(x))
     
  6. Sep 16, 2005 #5
    Another approach, graphically. An even function is symmetric to the y-axis, an odd function symmetric to the origin. Graph you functions and see what you come up with.
     
  7. Sep 16, 2005 #6

    shmoe

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    It's possible for a function to be neither even nor odd.
     
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