Simple question

  • #1
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Main Question or Discussion Point

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.
 

Answers and Replies

  • #2
shmoe
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Have you tried to apply the definitions of even and odd functions? Where does it get you?
 
  • #3
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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).
 
  • #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))
 
  • #5
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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.
 
  • #6
shmoe
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thenewbosco said:
...which is neither f(x) nor -f(x).
It's possible for a function to be neither even nor odd.
 

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