Back to School: Analyzing e^x and its Variations

[thenewbosco]

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.

 

[shmoe]

Have you tried to apply the definitions of even and odd functions? Where does it get you?

 

[thenewbosco]

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).

 

[Dr Avalanchez]

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))

 

[Jameson]

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.

 

[shmoe]

...which is neither f(x) nor -f(x).

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