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| Math Central | Quandaries & Queries |
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Question from Mohammed, a student: Hello 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
Thus
f(x) = -f(x)
so
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.
Harley
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