Math CentralQuandaries & Queries


Question from Mohammed, a student:


My question is :

Is it possible to a function to be both ( Even and Odd )

And if that possible what these functions

I'm looking forward to receiving the answer from you

Hi Mohammed,

Suppose x is some number in the domain of the function f and suppose f is both odd and even. Then

f(-x) = f(x) since f is even and
f(-x) - -f(x) since f is odd


f(x) = -f(x)


2f(x) = 0

and thus

f(x) = 0.

Hence the only function that is both odd and even is the function

f(x) = 0 for all x in the domain of f.


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